For a single exposure in radiography, a dual-layer flat-panel detector (DFD) can provide spectral images based on copper filtering or beam hardening, and efficiently utilize the transmitted x-ray photons to improve the detective quantum efficiency (DQE) performance. In this paper, we present a registration method for x-ray images acquired from DFD considering only spatial translations and scale factors. Note that the spatial translation difference between the upper and lower detector layers arises when attaching the layers, and the scale difference arises from the x-ray projection relative to the source and detector distances. The conventional registration methods have inconsistent estimate accuracies depending on the captured object scene even when using entire pixels, and have deteriorated frequency performance due to the interpolation method employed. The proposed method consists of two steps; the first step is conducting a spatial translation according to the Fourier shift theorem with a subpixel registration, and the second step is conducting a scale transformation using cubic interpolation to process the x-ray projections. To estimate the subpixel spatial translation, a maximum-amplitude method using a small portion of the slant-edge phantom is used. The performance of the proposed two-step method is first theoretically analyzed, and then observed by conducting extensive experiments and measuring the noise power spectrum and DQE. An example for registering chest images is also shown. For DFD, it is shown that the proposed method shows a better registration result than the conventional one-step registration.

In this paper we obtain some inequalities of Hermite-Hadamard type for composite convex functions. Applications for AG, AH-convex functions, GA, GG, GH-convex functions and HA, HG, HH-convex function are given. Applications for p, r-convex and LogExp functions are presented as well.

Machine unlearning, the process of selectively forgetting or removing the influence of specific data points from a machine learning model, is increasingly important for privacy and compliance with regulations like the GDPR. This paper explores the concept of exact unlearning, focusing on its implementation in models trained using convex and non-convex functions. Convex functions, due to their well-behaved optimization landscapes, lend themselves to efficient unlearning through methods such as inverse optimization, duality-based approaches, and incremental learning. In contrast, non-convex functions, common in deep learning models, present more complex challenges due to their multiple local minima and high-dimensional parameter spaces. Techniques like checkpoint-based retraining, gradient inversion, and meta-learning are discussed as viable, though computationally expensive, methods for non-convex exact unlearning. The paper also highlights real-world applications in fields such as finance and healthcare, where exact unlearning can enhance privacy and security without compromising model performance. Finally, it outlines key challenges and future research directions, particularly the need for more efficient unlearning algorithms in non-convex settings and the development of secure, adversarial-resistant methods for sensitive data removal.

In this paper we obtain some inequalities of Hermite-Hadamard type for composite convex functions. Applications for AG, AH-h-convex functions, GA, GG, GH-h-convex functions and HA, HG, HH-h-convex function are given.

This study focuses on a new class of functions called sub-b-s-preinvex, that is a generalization of sub-b-s-convex and preinvex functions, and discusses some of their properties. A new sub-b-s-preinvex programming is introduced and the sufficient conditions of optimality under this type of function is established.

This study explores the properties and behavior of bi-close-to-convex functions, introducing new subclasses defined by their relationship with fractional differential operator and bi-univalent functions. Using the Faber polynomial technique, we derive upper bounds for the n^{th} coefficient of functions in these classes. We also investigate the erratic behavior of initial coefficients in bi-close-to-convex functions, as characterized by the (λ,q)-fractional differintegral operator. Furthermore, we address Fekete-Szegö problems and present notable findings from our investigation, contributing to the continued growth and refinement of geometric function theory, yielding new insights and practical uses.

The paper's main goal is to introduce a novel type of interpolative convex contraction and build up some fresh findings for it using the interpolative convex contractions' progressive approach. We have established certain conclusions using orbitally S-complete and Suzuki type contractions in F-metric spaces. My research aims to examine the fixed point method's efficacy in solving fractional differential equation with boundary conditions.

In this paper, a new identity for the generalized fractional integral is defined, through which new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. We derive trapezoid and mid-point type inequalities connected to these generalized Hermite-Hadamard inequality.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η- convex function. Moreover, our results include several new and known results as special cases.

In this paper we establish several Hermite-Hadamard type integral inequalities for hyperbolic p-convex functions. Applications for special means are provided as well.

The algorithm described in this paper inherits the concepts of layered fusion, insertion, and set from four convex hull-based heuristic algorithms. It summarizes relevant definitions and theorems, proposes valuable research hypotheses, combines grouping and insertion, and innovatively introduces the practice of "grouped insertion."

Partial sums of analytic univalent functions and partial sums of starlike have been investigated extensively by several researchers. In this paper, we investigate a partial sums of convex harmonic functions that are univalent and sense preserving in the open unit disk.

In the present work we study the properties of geodesic sub-$ (\alpha,b,s) $-preinvex functions on Hadamard manifolds and establish some basic properties in both general and differential cases. Further, we study sufficient conditions of optimality and proved some new inequalities under geodesic sub-($ \alpha,b,s $)-preinvexity.

This article develops a duality principle and a related convex dual formulation suitable for a large class of models in physics and engineering. The results are based on standard tools of functional analysis, calculus of variations and duality theory. In particular, we develop applications to a model in non-linear elasticity.

This article develops duality principles and related convex dual formulations suitable for the local optimization of non-convex primal formulations for a large class of models in physics and engineering. The results are based on standard tools of functional analysis, calculus of variations and duality theory. In particular, we develop applications to a Ginzburg-Landau type equation.

The study examines n-balls, regular n-simplices, and n-orthoplices in real dimensions using novel recurrence relations that removed indefiniteness present in known formulas. They show that in the negative, integer dimensions volumes of n-balls are zero if n is even, positive if n = -4k - 1, and negative if n = -4k - 3, for natural k. Volumes and surfaces of n-cubes inscribed in n-balls in negative dimensions are complex, wherein for negative, integer dimensions they are associated with integral powers of the imaginary unit. The relations are continuous for n Î ℝ and show that the constant of π is absent for 0 ≤ n < 2. For n < -1 self-dual n-simplices are undefined in the negative, integer dimensions, and their volumes and surfaces are imaginary in the negative, fractional ones, and divergent with decreasing n. In negative, integer dimensions n-orthoplices reduce to the empty set, and their real volumes and imaginary surfaces are divergent in negative, fractional ones with decreasing n. Out of three regular, convex polytopes present in all natural dimensions, only n-orthoplices, n-cubes (and n-balls) are defined in the negative, integer dimensions.

In a one price economy, the Fundamental Theorem of Asset Pricing (FTAP) establishes that no-arbitrage is equivalent to the existence of an equivalent martingale measure. Such an equivalent measure can be derived as the normal unit vector of the hyperplane that separates the attainable gain subspace and the convex cone representing arbitrage opportunities. However, in two-price financial models (where there is a bid-ask price spread), the set of attainable gains is not a subspace anymore. We use convex optimization, and the conic property of this region to characterize the “No-Arbitrage” principle in financial models with the bid-ask price spread present. This characterization will lead us to the generation of a set of price factor random variables. Under such a set, we can find the lower and upper bounds (supper-hedging and sub-hedging bounds) for the price of any future cash flow. We will show that for any given cash flow, for which the price is outside the above range, we can build a trading strategy that provides one with an arbitrage opportunity. We will generalize this structure to any two-price finite-period financial model.

In this work, we introduce the class of h-MN-convex functions by generalizing the concept of MN-convexity and combining it with h-convexity. Namely, let M : [0, 1] → [a, b] be a Mean function given by M (t) = M (t; a, b); where by M (t; a, b) we mean one of the following functions: A_t (a, b) := (1 − t) a + tb, G_t (a, b) = a^1−tb^t and H_t (a, b) := $\frac{ab}{ta+\left(1-t\right)b}=\frac{1}{A_t\left(\frac{1}{a},\frac{1}{b}\right)}$ with the property that M (0; a, b) = a and M (1; a, b) = b. Let I, J be two intervals subset of (0, ∞) such that (0, 1) ⊆ J and [a, b] ⊆ I. Consider a non-negative function h : J → (0, ∞), a function f : I → (0, ∞) is said to be h-MN-convex (concave) if the inequality f (M (t; x, y)) ≤ (≥) N (h(t); f (x), f (y)), holds for all x, y ∈ I and t ∈ [0, 1]. In this way, nine classes of h-MN-convex functions are established, and therefore some analytic properties for each class of functions are explored and investigated. Characterizations of each type are given. Various Jensen’s type inequalities and their converses are proved.

In this work, several inequalities of Popoviciu type for h-MN-convex functions are proved, where M and N are denote to Arithmetic, Geometric and Harmonic means and h is a non-negative superadditive or subadditive function.

. In this paper, we introduce a series of definitions of generalized affine functions for vector-valued functions. We prove that our generalized affine functions have some similar properties with generalized convex functions. We present examples to show that our generalized affinenesses are different from one another, and also provide an example to show that our definition of presubaffinelikeness is non-trivial; presubaffinelikeness is the weakest generalized affineness introduced in this article. We work with optimization problems that are defined and taking values in linear topological spaces. We devote to the study of constraint qualifications, and derive some optimality conditions as well as a strong duality theorem. Our optimization problems have inequality constraints, equality constrains and abstract constraints; our inequality constraints are generalized convex functions and equality constraints are generalized affine functions.

This research paper presents a new test based on a novel approach for identifying clustered graphical passwords within the Passpoints scenario. Graphical authentication methods serve as a viable alternative to the conventional alphanumeric password-based authentication method, which is susceptible to known weaknesses arising from user-generated passwords of this nature. The test proposed in this study is based on estimating the distributions of the perimeter of the convex hull. This perimeter is calculated based on the points users select as passwords within an image measuring 1920 × 1080 pixels. The test is formulated once the optimal theoretical distributions that fit the data are identified. Evaluating the proposed test’s effectiveness involves estimating type I and II errors. In this study, we compare the effectiveness and efficiency of the proposed test with existing tests from the literature that can detect this type of pattern in Passpoints graphic passwords. Our findings indicate that the new test demonstrates a significant improvement in effectiveness compared to previously published tests. Furthermore, the joint application of the two tests also shows improvement. Depending on the significance level determined by the user or system, the enhancement results in a higher detection rate of clustered passwords, ranging from 0.1% to 8% compared to the most effective previous methods. This improvement leads to a decrease in the estimated probability of committing a type II error. In terms of efficiency, the proposed test outperforms several previous tests; however, it falls short of being the most efficient. It can be concluded that the newly developed test demonstrates the highest effectiveness and the second-highest efficiency level compared to other tests available in the existing literature for the same purpose.

Calculating a minimum-time trajectory requires the solving of a boundary value problem resulting from invocation of necessary conditions of optimality to set up a set of ordinary differential equations to solve the trajectory between the initial position and desired ending position with set constraints on the path between the two. This manuscript expresses the minimum time optimum trajectory between a satellite in a geosynchronous orbit and a target set on earth’s surface utilizing a non-rotating earth centric coordinate system. Expressing motion in coordinates of rotating reference frames necessitates transformation between reference frames, and one such transformation is embodied in the Direction Cosine Matrices (DCM) formed by a sequence of three successive frame rotations. Rotation about the local wing of an aerospace vehicle is almost never the pitch angle, yet modern application of kinematics often assumes such (with accompanying angular error). The same assertion is usually true about the nature of roll and yaw angles. This manuscript evaluates which sequence is the most advantageous for an object starting in space and then travels through the atmosphere to a target on the Earth’s surface. Simulation precision (validated by the quaternion normalization condition) reveals the so-called 132 rotation is the most accurate with an average error of 0.14° and a computational time of 0.013 seconds: resulting in a 97.95% increase in accuracy over the ubiquitous 321 “aerospace” rotation sequence and a 99.84% increase over the so-called 313 “orbital” rotation sequence. Utilizing the proposed optimal trajectory candidate yields a total flight time of 2 hours, 34 minutes and 46 seconds, or an average velocity of 3.85 kilometers per second, while impacting the target with a velocity of 11.54 kilometers per second.

In this work, an operator superquadratic function (in operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator convexity are pointed out. Equivalent statements of a non-commutative version of Jensen's inequality for operator superquadratic function are established. A generalization of the main result to any positive unital linear map is also provided.

In this study, based on a new quantum integral identity, the authors establish some quantum estimates of Hermite-Hadamard type inequalities for convex functions. These results generalize and improve some known results given in literatures.

The entropy of the partition generated by an n-tone music scale is proposed to quantify its regularity. The normalized entropy relative to a regular partition, and its complementary, here referred to as the bias, allow to analyze various conditions of similarity between an arbitrary scale and a regular scale. Interesting particular cases are scales having limited bias because their tones are distributed along interval fractions of a regular partition. The most typical case in music concerns partitions associated with well-formed scales generated by a single tone h. These scales are maximal even sets that combine two elementary intervals. Then, the normalized entropy depends on the number of tones as well as the relative size of both elementary intervals. When well-formed scales are refined, several nested families stand out with increasing regularity. It is proven that a scale of minimal bias, i.e. with less bias than those with fewer tones, is always a best rational approximation of log2h.

The unified Mittag-Leffler (ML) function is important factor in formulation of compact form of fractional integrals. In this paper estimations of integral operators, with the unified ML function as kernel are given. The Hadamard inequality in the form of fractional integrals is proved by considering refinement of convexities. These estimations provide various inequalities as refinements of recently published results.

In terahertz communication systems, lens antennas used in transceivers are basically plano-convex dielectric lenses. As the aperture increases and the focal length decreases, the thickness and mass of the plano-convex lens increase rapidly. Through theory and simulation, we designed a Fresnel lens suitable for the terahertz band to meet the requirements of large aperture and short focal length, and simulated the performance, advantages and disadvantages of the terahertz Fresnel lens. A 300GHz terahertz wireless communication system was built to verify the gain effect of the Fresnel lens antenna. The experimental results show that the Fresnel lens can amplify the signal in the terahertz band. The theoretical gain of a 30 cm Fresnel lens is 48.83dB, while the actual measured gain is approximately 45dB.

Some refinements and reverses of the Fejer's inequality for convex functions are given.

It is one of very important and basic problem in compute vision field that recovering depth information of objects from two-dimensional images. In view of the shortcomings of existing methods of depth estimation, a novel approach based on SIFT (the Scale Invariant Feature Transform) is presented in this paper. The approach can estimate the depths of objects in two images which are captured by an un-calibrated ordinary monocular camera. In this approach, above all, the first image is captured. All of the camera parameters remain unchanged, and the second image is acquired after moving the camera a distance d along the optical axis. Then image segmentation and SIFT feature extraction are implemented on the two images separately, and objects in the images are matched. Lastly, an object depth can be computed by the lengths of a pair of straight line segments. In order to ensure that the best appropriate a pair of straight line segments are chose and reduce the computation, the theory of convex hull and the knowledge of triangle similarity are employed. The experimental results show our approach is effective and practical.

This article develops duality principles applicable to originally non-convex primal variational formulations. More specifically, as a first application, we establish a convex dual approximate variational formulation for a non-linear Kirchhoff-Love plate model. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. We emphasize such a convex dual approximate formulation obtained may be applied to a large class of similar models in the calculus of variations. Finally, in the last section, we present a duality principle and respective convex dual formulation for a Ginzburg-Landau type equation.

In this paper, we consider a class of bilevel programming problems (abbreviated as, BLPP). Exploiting the generalized approximate convexity assumptions, we investigate the relations among the solutions of approximate Minty (respectively, Stampacchia) type variational inequalities (abbreviated as, AMTVI (respectively, ASTVI)), and the local ϵ-quasi solutions of the BLPP. Moreover, by employing the generalized Knaster–Kuratowski–Mazurkiewicz (abbreviated as, KKM)-Fan’s lemma, we derive some existence results for the solutions of approximate variational inequalities (abbreviated as, AVI), namely, AMTVI and ASTVI. A non-trivial example is given to highlight the importance of the established results. To the best of our knowledge, there is no research paper available in the literature that establishes relationships between the AVI and the BLPP under the assumptions of generalized approximate convexity in terms of limiting subdifferentials.

In the framework of a multiplicative metric space. We have discuss some Properties of convex structures in pseudo multiplicative metric space and have applied these properties toiobtain alfixed point results in complete pseudo. It would be interesting to prove some further results in such metric spaces with completeness property.

In this work, we establish some new Hermite-Hadamard type inequalities for convex functions via conformable fractional integral. Moreover, we show that through the conformable fractional integral we can find some new Hermite-Hadamard type inequalities for convex functions via the classical integrals.

Barrier coverage is a fundamental application in wireless sensor networks, which is widely used to protect a region through intruder detection for smart city. In this paper, we study a new branch of barrier coverage, named warning barrier coverage (WBC). Different from the classic barrier coverage, WBC has the inverse protect direction, which protects unexpected visitors by warning them away from the region enclosed by sensor barriers. The WBC holds a promising prospect in many danger keep out applications for smart city. For example, a WBC can enclose the debris area in the sea and alarm any approaching ships in order to avoid their damaging propellers. One special feature of WBC is that the target region is usually dangerous and its boundary is previously unknown. Hence, the scattered mobile nodes need to detect the boundary and form the barrier coverage themselves. It is challenging to form these distributed sensor nodes into a barrier because a node can sense only the local information and there is no global information of the unknown region or other nodes. To this end, we propose a novel solution AutoBar for mobile sensor nodes to automatically form a WBC for smart city. To pursue the high coverage quality, we theoretically derive the optimal distribution pattern of sensor nodes using convex theory. Based on the analysis, we design a fully distributed algorithm that enables nodes to collaboratively move towards the optimal distribution pattern. In addition, AutoBar is able to reorganize the barrier even any node is broken. To validate the feasibility of AutoBar, we develop the prototype of the specialized mobile node, which consists of two kinds of sensors: one for boundary detection and another for visitor detection. Based on the prototype, we conduct extensive real trace driven simulations in various smart city scenarios. Performance results demonstrate that AutoBar outperforms the existing barrier coverage strategies in terms of coverage quality, formation duration, and communication overhead.

In this study we introduce the new classes $\mathcal{M}_{\alpha}(\sin)$ and $\mathcal{M}_{\alpha}(\cos)$ of $\alpha$-convex functions associated with sine and cosine functions. Also, we obtain the initial coefficient bounds for the first five coefficients of the functions that belong to these classes. Further, we determine the upper bound of Zalcman functional for the class $\mathcal{M}_{\alpha}(\cos)$ for the case $n=3$, showing that the Zalcman conjecture holds for this value. Moreover, the problem of the Fekete-Szeg\H{o} functional estimate for these classes is studied.

Facial appearance significantly influences several life outcomes, and a convex profile often prompts patients to seek treatment to enhance their facial esthetics. This study aimed to assess the facial appearance outcomes of combined orthodontic and orthognathic intervention compared to orthodontic camouflage treatment in convex facial profile individuals. The study sample comprised 36 consecutively selected Class II Division 1, convex facial profile patients. Two groups of 18 non-growing patients with similar characteristics were compared. Group A was treated with orthodontics and orthognathic surgery, whereas Group B with orthodontics exclusively. Pre- and post-treatment profile and frontal facial photographs were presented simultaneously to orthodontists, oral and maxillofacial surgeons, convex profile patients, and laypeople, asking them to assess changes in facial appearance. Considerable positive changes in facial appearance were perceived for Group A, compared to no changes for Group B, with a 17/100 VAS units difference. The rater groups demonstrated a high degree of consistency (ICC > 0.88). Multivariate analysis revealed significant differences in perceived changes between the two treatment groups (F = 14.63, P < 0.001, Pillai's Trace = 0.36, partial η2 = 0.36), with no significant effects from the rater group (P > 0.05). Similar results were evident when only profile photos were rated (P > 0.05). The combined orthodontic and surgical intervention is an efficient approach for the enhancement of facial appearance in convex profile cases. On the contrary, orthodontic treatment alone has no such impact. These findings should be properly communicated during patient consultation and considered for treatment planning.

This paper surveys the landscape of security and data attacks on machine unlearning, with a focus on financial and e-commerce applications. We discuss key privacy threats such as Membership Inference Attacks and Data Reconstruction Attacks, where adversaries attempt to infer or reconstruct data that should have been removed. In addition, we explore security attacks including Machine Unlearning Data Poisoning, Unlearning Request Attacks, and Machine Unlearning Jailbreak Attacks, which target the underlying mechanisms of unlearning to manipulate or corrupt the model. To mitigate these risks, various defense strategies are examined, including differential privacy, robust cryptographic guarantees, and Zero-Knowledge Proofs (ZKPs), offering verifiable and tamper-proof unlearning mechanisms. These approaches are essential for safeguarding data integrity and privacy in high-stakes financial and e-commerce contexts, where compromised models can lead to fraud, data leaks, and reputational damage. This survey highlights the need for continued research and innovation in secure machine unlearning, as well as the importance of developing strong defenses against evolving attack vectors.

This article develops duality principles and numerical results for a large class of non-convex variational models. The main results are based on fundamental tools of convex analysis, duality theory and calculus of variations. More specifically the approach is established for a class of non-convex functionals similar as those found in some models in phase transition. Finally, in some sections we present concerning numerical examples and the respective softwares.

A class of controlled plants, whose dynamics is governed by a vector system of ordinary differential equations with a partially known right-hand side, is considered. The state variables and their velocities are assumed to be measurable. The aim is to design a controller which minimizes a loss function under certain constraints which arguments is the current state of the controlled plant. The designed control action is admitted to be a function of the current sub-gradient only, which supposed to be measurable on-line. The control design is based on ASG (Average Sub-Gradient method) — version of Integral Sliding Mode (ISM) concept, aimed to minimize on average a given convex (not obligatory strongly convex) cost function of the current state under a set of given constraints. An optimization type algorithm is developed and analyzed using ideas of SDM technique. The main results consist in proving the reachability of the "desired regime" (nonstationary analogue of sliding surface) from the beginning of the process and obtaining an explicit upper bound for the averaged loss function decrement, that is, the averaged in time functional convergence is proven and the rate of such convergence is estimated.

The common dolphin is the second most bycaught species in Korean waters. To provide key information about their habitat boundaries and hotspots for spatial conservation and management, the spatial use of this species was examined using data obtained from sighting and bycatch surveys of cetacean during the past 20 years. The 95% minimum convex polygon and 95% density contour of fixed kernel suggested that the boundary of home range of common dolphins is limited to the coastal region (Busan-Sokcho) of the East Sea/Sea of Japan. From 50% density contours dawn by kernel density estimation, it was suggested that their hotspots are around the cost of Ulsan-Pohang, Doghae, and Sokcho within the home range. Common dolphins are not at all distributed in the Yellow Sea. Hence, shallow waters, such as the coastal region of the Yellow Sea, are not suitable habitats for common dolphins.

High-dimensional measurement error data are becoming more prevalent across various fields. Research on measurement error regression models has gained increasing attention due to the risk of drawing inaccurate conclusions if measurement errors are ignored. When the dimension p is larger than the sample size n, it is challenging to develop statistical inference methods for high-dimensional measurement error regression models due to the existence of bias, nonconvexity of objective function, high computational cost and many other difficulties. Over the past few years, some works have overcome the aforementioned difficulties and proposed several statistical inference methods. This paper mainly reviews the current development on estimation, hypothesis testing and variable screening methods for high-dimensional measurement error regression models and shows the theoretical results of these methods with some directions worthy of exploring for future research.

In this paper, we propose an efficient numerical computation method of reduced-order controller design for linear time-invariant systems. The design problem is described by linear matrix inequalities (LMIs) with a rank constraint on a structured matrix, due to which the problem is NP-hard. Instead of the heuristic method that approximates the matrix rank by the nuclear norm, we propose a numerical projection onto the rank-constrained set based on the alternating direction method of multipliers (ADMM). Then the controller is obtained by alternating projection between the rank-constrained set and the LMI set. We show the effectiveness of the proposed method compared with existing heuristic methods, by using 95 benchmark models from the COMPLeib library.

In this article, the new Hermite–Hadamard type inequalities are studied via generalized s-convexity on fractal sets. These inequalities derived on fractal sets are shown to be the generalized s-convexity on fractal sets. We proved that the absolute values of the first and second derivatives for the new inequalities are the generalization of s-convexity on fractal sets.

In this article, the new Hermite–Hadamard type inequalities are studied via generalized s-convexity on fractal sets. These inequalities derived on fractal sets are shown to be the generalized s-convexity on fractal sets. We proved that the absolute values of the first and second derivatives for the new inequalities are the generalization of s-convexity on fractal sets.

In this paper, we introduce two subclasses of analytic and Spirallike functions and investigate convolution properties, the necessary and sufficient condition, coefficient estimates and inclusion properties for these classes .

In this paper, we investigate a new subclass of univalent functions defined by a generalized differential operator, and obtain some interesting properties of functions belonging to the class R^m λµ ( α, β, γ, υ ).

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η-convex function. Moreover, our results include several new and known results as special cases.

In this paper, a distributed algorithm is proposed to solve a consensus convex optimization problem. It is a Jacobi-proximal alternating direction method of multipliers with a damping parameter $\gamma$ in the iteration of multiplier. Compared with existing algorithms, it has the following nice properties: (1) The restriction on proximal matrix is relaxed substantively, thus alleviating the weight of the proximal term. Therefore, the algorithm has a faster convergence speed. (2) The convergence analysis of the algorithm is established for any damping parameter $\gamma\in(0,2]$, which is larger ones in the literature. In addition, some numerical experiments and an application to a logistic regression problem are provided to validate the effectiveness and the characteristics of the proposed algorithm.

In the present paper, we introduced and study a new class of harmonic univalent functions on unit disc U. also we obtain coefficient conditions, extreme points, convolution condition for the above class of harmonic univalent functions.

This study analyses the short-run hydro generation scheduling for the wind power differences from the contracted schedule. The approach for construction of the joint short-run marginal cost curve for the hydro-wind coordinated generation is proposed and applied on the real example. This joint short-run marginal cost (SRMC) curve is important for its participation in the energy markets and for economic feasibility assessment of such coordination. The approach credibly describes the short-run marginal costs which this coordination bears in “real life”. The approach is based on the duality framework of a convex programming and as a novelty combines the shadow price of risk mitigation capability and the water shadow price. The proposed approach is formulated as a stochastic linear program and tested on the case of the Vinodol hydropower system and the wind farm Vrataruša in Croatia. The result of the case study is a family of 24 joint short-run marginal cost curves.

Non-convex optimization is a critical tool in advancing machine learning, especially for complex models like deep neural networks and support vector machines. Despite challenges such as multiple local minima and saddle points, non-convex techniques offer various pathways to reduce computational costs. These include promoting sparsity through regularization, efficiently escaping saddle points, and employing subsampling and approximation strategies like stochastic gradient descent. Additionally, non-convex methods enable model pruning and compression, which reduce the size of models while maintaining performance. By focusing on good local minima instead of exact global minima, non-convex optimization ensures competitive accuracy with faster convergence and lower computational overhead. This paper examines the key methods and applications of non-convex optimization in machine learning, exploring how it can lower computation costs while enhancing model performance. Furthermore, it outlines future research directions and challenges, including scalability and generalization, that will shape the next phase of non-convex optimization in machine learning.

In the Internet of Things (IoT) era, Mobile Edge Computing (MEC) significantly enhances the efficiency of smart devices but is limited by battery life issues. Wireless Power Transfer (WPT) addresses this issue by providing a stable energy supply. However, effectively managing overall energy consumption remains a critical and under-addressed aspect for ensuring the network’s sustainable operation and growth. In this paper, we consider a WPT-MEC network wit user cooperation to migrate the double near-far effect for the mobile node (MD) far from the base station. We formulate the problem of maximizing long-term computation rates under a power consumption constraint as a multi-stage stochastic optimization (MSSO) problem. This approach is tailored for a sustainable WPT-MEC network, considering the dynamic and varying MEC network environment, including randomness in task arrivals and fluctuating channels. We introduce a virtual queue to transform the time-average energy constraint into a queue stability problem. Using the Lyapunov optimization technique, we decouple the stochastic optimization problem into a deterministic problem for each time slot, which can be further transformed into a convex problem and solved efficiently. Our proposed algorithm works efficiently online without requiring further system information. Rigorous mathematical analysis shows that our algorithm achieves O(1/V),O(V) trade-off between computation rate and queues stability. Extensive simulation results demonstrate that our proposed algorithm outperforms baseline schemes, achieving approximately 4% enhancement while maintain the queues stability.

Mobile Edge Computing (MEC) integrated with Wireless Power Transfer (WPT) is emerging as a promising solution to reduce task delays and extend the battery life of Mobile Devices (MDs). Cooperative user communication, or relay technology, enhances communication efficiency for users located far from the base station by mitigating the double near-far effect caused by distance. This is considered a key technology in Beyond 5G (B5G) and future communication systems. In this paper, we focus on maximizing the long-term energy efficiency (EE) of a user-cooperation WPT-MEC system, while taking into account the uncertain load dynamics at the edge MD and the time-varying state of the wireless channel. The joint optimization of wireless charging time fraction, MD offloading duration, helper node processing time, and transfer power decision presents significant challenges due to the coupling of data offloading among cooperative users and a volatile system environment. To address these challenges, we formulate the problem as a stochastic programming problem and propose an online control algorithm, DOUCA, to solve it. Our approach utilizes Dinkelbach’s method and Lyapunov optimization theory to decouple the sequential decision problem into a deterministic sub-problem for each time slot. For the sub-problem, we use variable substitution to convert the non-convex problem into a convex one, containing only a small number of variables, which can be efficiently solved. Furthermore, we provide a mathematical analysis of our algorithm’s performance. Extensive simulation results demonstrate the effectiveness of our proposed algorithm, as evidenced by an impressive energy efficiency improvement of over 20% compared to benchmark methods. Our algorithm also achieves a trade-off between EE and system stability.

The study shows that the volumes and surfaces of $n$-balls, $n$-simplices, and $n$-orthoplices are holomorphic functions of $n$, which makes those objects omnidimensional, that is well defined in any complex dimension. Applications of these formulas to the omnidimensional polytopes inscribed in and circumscribed about $n$-balls reveal previously unknown properties of these geometric objects. In particular, for $0 < n < 1$, the volumes of the omnidimensional polytopes are larger than those of circumscribing $n$-balls, and both their volumes and surfaces are smaller than those of inscribed $n$-balls. The surface of an $n$-simplex circumscribing unit diameter $n$-ball is spirally convergent to zero with real $n$ approaching negative infinity but first has a local maximum at $n=-3.5$. The surface of an $n$-orthoplex circumscribing unit diameter $n$-ball is spirally divergent with real $n$ approaching negative infinity but first has a local minimum at $n=-1.5$, where its real and imaginary parts are equal to each other; similarly, as its volume, where the similar local minimum occurs at $n=-3.5$. Reflection functions for volumes and surfaces of these polytopes inscribed in and circumscribed about $n$-balls are proposed. symmetries of products and quotients of volumes in complex dimensions $n$ and $-n$ and of surfaces in complex dimensions $n$ and $2-n$ are shown to be independent of the metric factor and the gamma function. Specific symmetries also hold between volumes and surfaces in dimensions $n = -1/2$ and $n = 1/2$.

In this paper, we introduce a new iteration scheme, named as the S**-iteration scheme, for approximation of fixed point of the nonexpansive mappings. This scheme is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our instigated scheme and give a numerical example to vindicate our claim. We also put forward some weak and strong convergence theorems for Suzuki's generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Our results comprehend, improve, and consolidate many results in the existing literature.

In the article, by applied the concept of strongly convex function and one known identity, we establish several Ostrowski type inequalities involving conformable fractional integrals. As applications, some new error estimations for the midpoint formula are provided as well.

In this work, we explore Conjecture 1 proposed in the newly released pioneering paper “Volatility transformers: an optimal transport-inspired approach to arbitrage-free shaping of implied volatility surfaces” by Zetocha Valer, which posits that the “One-X” property is both a necessary and sufficient condition for convex order between non-negative continuous strictly increasing distributions with the same mean. We provide a counterexample demonstrating that the conjecture, as originally stated, does not hold. By examining stochastic orders, particularly the increasing convex order, and the “One-X” property, we propose an enhanced version of the conjecture which is shown to be valid. Furthermore, we discuss the implications of these findings in the context of equity implied volatility fitting and the construction of implied volatility surfaces, highlighting the challenges posed by real-market conditions. In the end, we propose several applications in implied volatility surface construction or simulation.

Input noise causes inescapable bias to the weight vectors of the adaptive filters during the adaptation processes. Moreover, the impulse noise at the output of the unknown systems can prevent bias compensation from converging. This paper presents a robust bias compensation method for a sparse normalized quasi-Newton least-mean (BC-SNQNLM) adaptive filtering algorithm to address this issue. We have mathematically derived the biased-compensation terms in an impulse noisy environment. Inspired by the convex combination of adaptive filters' step sizes, we propose a novel variable-mixing-norm method to accelerate the convergence for our BC-SNQNLM algorithm, which is referred to as BC-SNQNLM-VMN. Simulation results confirm that the proposed method significantly outperforms other comparative works regarding normalized mean-squared deviation (NMSD) in the steady state.

This paper addresses the optimal stochastic allocation of Distributed Energy Resources in distribution Networks. Typically, uncertain problems are analyzed in multi-stage formulations including case generation routines, resulting in computationally exhaustive programs. In this article, two probabilistic approaches are proposed resulting in a single-stage, convex, stochastic optimal power flow problem: The Range-Probability Optimization (RPO) and Value-Probability Optimization (VPO). The RPO maximizes probabilities within a range of uncertainty, whilst the VPO optimizes the values of the random variables and maximizes their probabilities. Random variables are modeled with hourly measurements fitted to the logistic distribution. These formulations were tested on two systems and compared against the deterministic case built from expected values. Results indicate that assuming deterministic conditions ends in highly underestimated losses. The RPO showed that by including a ±10 % uncertainty, the losses can be increased up to 40 % with up to −72 % photovoltaic capacity, depending on the system, whereas the VPO resulted in up to 85 % increases in power losses despite PV installations, with 20 % greater probabilities in average. By implementing any of the proposed approaches, it was possible to obtain more probable upper envelopes in the objective, avoiding case generation stages and heuristic methods.

In this paper, we prove that the sub convexlikeness introduced by V. Jeyakumar [1], and the subconvexlikeness defined in V. Jeyakumar [2] are equivalent in loccallly convex topological spaces. And then, we work with set-valued vector optimization problems and obtain some vector saddle-point theorems and vector Lagrangian theorems.

In this paper we analyze and propose new method and algorithm of selecting the optimal labor time as a function of skills following our main references Mirrlees (1971), Saez (2001) and Stancheva (2014). The optimal labor time is a situation when the utility function of individual reaches a maximum. One of the main differences with Saez (2001) is our algorithm for creation the skill distribution

In this paper we survey some recent results due to the author concerning various inequalities and approximations for the finite Hilbert transform of a function belonging to several classes of functions, such as: Lipschitzian, monotonic, convex or with the derivative of bounded variation or absolutely continuous. More accurate estimates in the case that the higher order derivatives are absolutely continuous, are also provided. Some quadrature rules with error bounds are derived. They can be used in the numerical integration of the finite Hilbert transform and, due to the explicit form of the error bounds, enable the user to predict a priory the accuracy.

In this paper, some convexity properties and some inequalities for the (p,k)-analogue of the Gamma function, Г_p,k(x) are given. In particular, a (p,k)-analogue of the celebrated Bohr-Mollerup theorem is given. Furthermore, a (p,k)-analogue of the Riemann zeta function, ζ_p,k(x) is introduced and some associated inequalities are derived. The established results provide the (p,k)-generalizations of some known results concerning the classical Gamma function.

In this paper, we present a full coverage path planning (CPP) algorithm for the marine surveys conducted in the convex polygon shaped search area. The survey is supposed to carry out by torpedo-type AUVs (autonomous underwater vehicles). Due to their nonholonomic mechanical characteristics, these vehicles have nonzero minimum turning radius. For any given polygon shaped search area, it can always be partitioned into one or more convex polygons. With this in mind, this paper proposes a novel search algorithm called CbSPSA (Calculation based Shortest Path Search Algorithm) for full coverage of any given convex polygon shaped search area. By aligning the search inter-tracks alongside the edge with the minimum height, we can guarantee the minimum number of the vehicle’s turns. In addition, the proposed method can guarantee the planned path is strictly located inside the polygon area without overlapped or crossed path lines, and also has the total path length as short as possible. Considering the vehicle’s nonzero minimum turning radius, we also propose a sort of smoothing algorithm to smooth the waypoint path searched by CbSPSA so as for the vehicle to exactly follow it. The smoothed path is also guaranteed to be strictly located inside the polygon. Numerical simulation analyses are also carried out to verify the effectiveness of the proposed schemes.

Utilizing unmanned aerial vehicles (UAVs) to facilitate wireless communication has emerged as a viable and promising strategy aimed at enhancing both current and prospective wireless systems. This approach offers many advantages by establishing line-of-sight connections, optimizing operational efficiency, and enabling flexible deployment capabilities in various terrains. Thus, in this paper, we investigate UAV communication in a relaying network in which a UAV helps communication between a source and two destination users while flying to a location. To have a complete view of our proposed system, we consider both orthogonal multiple access as OFDM and non-orthogonal multiple access (NOMA) scenarios. Moreover, we apply successive convex optimization (SCO) and the Block-coordinate gradient descent (BCGD) for the sum-rate optimization problems to improve the system performance under constraints of total bandwidth and total power at the ground base station and UAV. The experimental results validate that the achievable secrecy rates are notably enhanced by using our proposed algorithms and show optimal trends for critical parameters, such as transmit powers, the flight trajectory and speed of UAV, and resource allocation of OFDM and NOMA.

In this study, we first discover some new concept coordinated UD-convex mappings with fuzzy-number values. After that, we look into Hermite-Hadamard type inequalities via fuzzy-number-valued coordinated UD-convex fuzzy-number-valued mapping (coordinated UD-convex FNVM). In the case of coordinated UD-convex FNVM, novel conclusions are derived by making particular decisions in recently proven inequalities. Additionally, it is demonstrated that the recently discovered inequalities are expansions of comparable findings in the literature. It is important to note that the main outcomes are validated by nontrivial examples.

Clustering algorithms for multi-database mining (MDM) rely on computing $(n^2-n)/2$ pairwise similarities between $n$ multiple databases to generate and evaluate $m\in[1, (n^2-n)/2]$ candidate clusterings in order to select the ideal partitioning which optimizes a predefined goodness measure. However, when these pairwise similarities are distributed around the mean value, the clustering algorithm becomes indecisive when choosing what database pairs are considered eligible to be grouped together. Consequently, a trivial result is produced by putting all the $n$ databases in one cluster or by returning $n$ singleton clusters. To tackle the latter problem, we propose a learning algorithm to reduce the fuzziness in the similarity matrix by minimizing a weighted binary entropy loss function via gradient descent and back-propagation. As a result, the learned model will improve the certainty of the clustering algorithm by correctly identifying the optimal database clusters. Additionally, in contrast to gradient-based clustering algorithms which are sensitive to the choice of the learning rate and require more iterations to converge, we propose a learning-rate-free algorithm to assess the candidate clusterings generated on the fly in a fewer upper-bounded iterations. Through a series of experiments on multiple database samples, we show that our algorithm outperforms the existing clustering algorithms for MDM.

In this paper, we present a complete, flexible and safe convex-optimization-based method to solve speed planning problems over a fixed path for autonomous driving in both static and dynamic environments. Our contributions are five fold. First, we summarize the most common constraints raised in various autonomous driving scenarios as the requirements for speed planner developments and metrics to measure the capacity of existing speed planners roughly for autonomous driving. Second, we introduce a more general, flexible and complete speed planning mathematical model including all the summarized constraints compared to the state-of-the-art speed planners, which addresses limitations of existing methods and is able to provide smooth, safety-guaranteed, dynamic-feasible, and time-efficient speed profiles. Third, we emphasize comfort while guaranteeing fundamental motion safety without sacrificing the mobility of cars by treating the comfort box constraint as a semi-hard constraint in optimization via slack variables and penalty functions, which distinguishes our method from existing ones. Fourth, we demonstrate that our problem preserves convexity with the added constraints, thus global optimality of solutions is guaranteed. Fifth, we showcase how our formulation can be used in various autonomous driving scenarios by providing several challenging case studies in both static and dynamic environments. A range of numerical experiments and challenging realistic speed planning case studies have depicted that the proposed method outperforms existing speed planners for autonomous driving in terms of constraint type covered, optimality, safety, mobility and flexibility.

In the present paper we introduce three new classes of bi-univalent functions connected with Gregory coefficients. For functions in each of these three bi-univalent function classes we have derived the estimates of the Taylor--Maclaurin coefficients $\left|a_{2}\right|$ and $\left|a_{3}\right|$ and Fekete-Szeg\H{o} functional problems for functions belonging to these new subclasses. We defined three subclasses of the class of the bi-univalent functions $\Sigma$, namely $\mathfrak{HG}_{\Sigma}$, $\mathfrak{GM}_{\Sigma}(\mu)$ and $\mathfrak{G}_{\Sigma}(\lambda)$ by using the subordinations with the function whose coefficients are Gregory's numbers. First, we proved that these classes are not empty, i.e. contains other functions than the identity one. Using the well-known Carath\'eodory Lemma for the functions with real positive parts in the open unit disk, together with an estimation due to P. Zaprawa (see https://doi.org/10.1155/2014/357480) and another one of Libera and Zlotkiewicz, we gave upper bounds for the above mentioned initial coefficients and for the Fekete-Szeg\H{o} functionals. The main results are followed by some particular cases, and the novelty of the definitions and the proofs could involve further studies for such type of similarly defined subclasses.

This research takes Cuiwei Village in Qianshan District of Zhuhai City as an example. Through field research, the village is investigated and analyzed, and the street scale, spatial structure, functional characteristic streets, internal commercial distribution forms, and functions of Cuiwei Historic District are studied. analysis. On this basis, based on the convex space method and the line-of-sight analysis method in the space syntax theory, with the help of Depthmap software, the complex street node, that is, the space of the two nodes A and B, is established through the establishment of a visual field model. It includes the analysis of the integration degree of the horizon, the concentration of the horizon, the connection value of the horizon and the spatial characteristics of the historical area, as well as the traditional buildings that are the most representative of the village, namely the Three Kings Temple and the Webster's Mansion. When R=N and radius R=3, observe the changes in the two parameters of the visual integration and visual depth of the two historical buildings. And with the help of Baidu Time Machine photos in different periods to observe and record the changes in the store and the characteristics of people's behavior, and draw conclusions.

Our aim in this paper is to establish some new Hermite-Hadamard- Mercer type integral inequalities by utilizing the fractional proportional-integral operators.For this purpose, Hermite-Hadamard-Mercer inequalities for di¤er- antiable mappings whose derivatives in absolute value are convex.

In this paper, we study a three step iterative scheme to approximate fixed points of Suzuki's generalized non-expansive mappings. We establish some weak and strong convergence results for such mappings in uniformly convex Banach spaces. Further, we show numerically that iterative scheme (1.8) converges faster than some other known iterations for Suzuki's generalized non-expansive mappings. To support our claim, we give an illustrative example and approximate fixed points of such mappings using Matlab program. Our results are new and generalize several relevant results in the literature.

In this study, we consider a Lambert series whose coefficients are the sum of divisors function. Utilizing the Lambert series in the sequel we introduce a normalized linear operator JR_(α,β) (z) by applying the convolution with Rabotnov function. We then, acquire sufficient conditions for JR_(α,β) (z) to be Univalent, Starlike and Convex respectively. In each component of this study, we expand the derived results by applying two Robin's inequalities, one of which is equivalent to the Riemann hypothesis.

Abstract—The static and fatigue analysis of plates with holes, made of 2D woven roving composites, is conducted. The parametrization of convex holes is proposed. Experimental results of specimens without holes and with different shapes of notches are discussed. The fatigue behaviour is considered with the use of the low cycle fatigue method. The analysis is supplemented by the numerical finite element modeling. The present work is an extension of the results discussed in the literature. The finite element modeling of plates with holes is presented in details in Ref [1-3] including also the problems of the accuracy. The experimental results and the form of specimens are shown in Ref [4]. Two parametrical description of static and fatigue behaviour of plates with holes characterizes the goal and the novelty of the paper. The fuzzy approach is employed to reduce the number of experimental data [5].

Rapid search and localization for nuclear sources can be an important aspect in preventing human harm from illicit material in dirty bombs or from contamination. In the case of a single mobile radiation detector, there are numerous challenges to overcome such as weak source intensity, multiple sources, background radiation, and the presence of obstructions, i.e., a non-convex environment. In this work, we investigate the sequential decision making capability of deep reinforcement learning in the nuclear source search context. A novel neural network architecture (RAD-A2C) based on the actor critic (A2C) framework and a particle filter gated recurrent unit for localization is proposed. Performance is studied in a randomized 20 x 20 m convex and non-convex environment across a range of signal-to-noise ratio (SNR)s for a single detector and single source. RAD-A2C performance is compared to both an information-driven controller that uses a bootstrap particle filter and to a gradient search (GS) algorithm. We find that the RAD-A2C has comparable performance to the information-driven controller across SNR in a convex environment and at lower computational complexity per action. The RAD-A2C far outperforms the GS algorithm in the non-convex environment with greater than 95% median completion rate for up to seven obstructions.

We investigated the radioclinical outcomes of naviculectomy and limited/tailored soft-tissue releases in a short series of ambulatory children with complex/intractable congenital vertical talus subsets namely neglected, multiple operated and recurrent patients. We postulated that this technique will yield satisfactory radioclinical outcomes and minimal complications because it avoids extensive surgical release/trauma that is otherwise classically recommended for complex congenital vertical talus (CVT). The cohort consisted of five -four boys, one girl- complex CVT children with neglected, multiple operated and/or recurrent subsets. Patients were included if manipulative casting techniques were deemed unlikely to produce a plantigrade foot. Patients underwent naviculectomy with variable on-demand limited soft tissue releases. Two patients had bilateral affection and two had a non-idiopathic aetiology. The mean age was 5.2 years (4 to 6.25) and mean follow-up was 2.3 years (1 to 3). We reported satisfactory outcomes as per foot posture, function, overall parent satisfaction including pain and radiography per lateral views of talar-axis-first metatarsal base angle on the short/intermediate term. Whereas manipulative casting is unlikely to yield lasting outcomes in ambulatory children with complex subsets of CVT, extensive surgical soft-tissue releases have unfavourable long-term complications. As a substitute, naviculectomy as a form of resection arthroplasty created a practical and affordable third way between manipulative casting with minimally invasive surgery and the extensive surgical soft tissue releases on the short/intermediate term.

The evaluation of geometric defects is necessary in order to maintain the integrity of structures over time. These assessments are designed to detect damages of structures and ideally help inspectors to estimate the remaining life of structures. Current methodologies for monitoring structural systems, while providing useful information about the current state of a structure, are limited in the monitoring of defects over time and in linking them to predictive simulation. This paper presents a new approach to the predictive modeling of geometric defects. A combination of segmented from point clouds are parametrized using the convex hull algorithm to extract features from detected defects, and a stochastic dynamic model is then adapted to these features to model the evolution of the hull over time. Describing a defect in terms of its parameterized hull enables consistent temporal tracking for predictive purposes, while implicitly reducing data dimensionality and complexity as well. In this study, 2D point clouds analogous to information derived from point clouds were first generated over simulated life-cycles. The evolutions of point cloud hull parameterizations were modeled as stochastic dynamical processes via autoregressive integrated moving average (ARIMA) and vectorized autoregression (VAR) and compared against ground truth. The results indicate that this convex hull approach provides consistent and accurate representations of defect evolution across a range of defect topologies and is reasonably robust to noisy measurements, however assumptions regarding the underlying dynamical process play a significant the role in predictive accuracy. The results were then validated on experimental data from fatigue testing with high accuracy. Longer term, the results of this work will support finite element model updating for predictive analysis of structural capacity.

It is known that the class of p-normed spaces (0 < p ≤ 1) is an important generalization of usual normed spaces with rich topological and geometrical structure, but the most of tools and general principles in nature with nonlinearity have not been developed yet, thus the main goal of this paper is to develop tools for nonlinear analysis under the framework of p-vector spaces. In particular, we first develop the general fixed point theorems which provide solutions to answer Schauder conjecture since 1930’s in the affirmative for p-vector spaces when p = 1 (which is just general topological vector spaces); then the one best approximation result for upper semi-continuous mappings is given, which is used as a powerful tool to establish fixed points for non-self set-valued mappings with either inward or outward set conditions; and finally we establish comprehensive existence results of solutions for Birkhoff-Kellogg Problems, and the general principle of nonlinear alternative by including Leray-Schauder alternative and related results. The results given in this paper not only include the corresponding results in the existing literature as special cases, but also expected to be useful tools for the study of nonlinear problems arising from theory to practice.