Information security plays a major role in the dynamics of today’s interconnected world. Despite the successful implementation and effectiveness of modern cryptographic techniques, their inherent limitations can be exploited by quantum computers. In this article we discuss Grover’s quantum searching algorithm and its impact on the security of modern symmetric ciphers. More specifically, we present its formal description and give an implementation of the algorithm using IBM’s Qiskit framework, which allows us to simulate and run the program on a real device. The developed program is modular and scalable, managing to properly run on any input state. We compare the performance of the algorithm running on the local simulator against its execution on a quantum processor from IBM’s lineup, noting the discrepancies between the results due to physical characteristics of the chip.

Radio Frequency Identification (RFID) devices use radio waves to relay identifying information to an electronic reader using low-cost RFID Tag. RFID is expected to replace the conventional bar-code identification system due to its advantage like real-time recognition of a considerable number of objects. However, in RFID systems an attacker can get the tag that may lead to various security threats, and the limited computation power of RFID tags can cause delay. Lightweight authentication protocols proposed using cryptographic algorithms (one-way hash function, symmetric key encryption/decryption, and exclusive-OR) in order to cope with these problems. One such lightweight cryptographic protocol has been presented by Gope and Hwang using RFID systems. However, it analyzed in this article that their protocol is infeasible and vulnerable to Collision Attack, Denial-of-service (DoS), and Stolen verifier Attacks. A realistic, lightweight authentication protocol has been presented in this article to ensure protection against the mentioned attacks for IoT based RFID system. The proposed protocol has been formally analyzed using BAN logic and ProVerif as well as also analyzed informally using security requirement. The results show that the proposed protocol outperforms the existing protocols not only in security enhancements but also in terms of computation and communication complexity. Furthermore, the proposed protocol has also been analyzed for storage complexity.

In this work we study the energy consumption by various modern secured hash functions (MD2, MD5, SHA-1, and SHA-2) and modern symmetric key encryption protocols (Blowfish, DES, 3DES, and AES) from the algorithmic perspective. We identify various parameters that moderate energy consumption of these hashes and protocols. Our work is directed towards redesigning or modifying these algorithms to make them consume lesser energy. As a first step, we try to determine the applicability of the asymptotic energy complexity model by Roy et. al. on these hashes and protocols. Specifically, we try to observe whether parallelizing the access of blocks of data in these algorithms reduces their energy consumption based on the energy model. Our results confirm the applicability of the energy model on these hashes and protocols. Our work is motivated by the relevance and importance of cryptographic hashes and symmetric key protocols for modern ICT (Information and Communication Technology), and ICT enabled industry to keep them protected from dynamically changing threat scenarios. Hence the design of more energy efficient hashes and protocols will definitely contribute in reducing the ICT energy consumption that is continuously increasing.

Compressive sensing (CS) is a technique that allows a signal vector to be reconstructed with a number of linear measurements far fewer than its size. In this study, optical hybrid cryptography with simultaneous compressive sensing based on orthogonal matching pursuit (OMP) is proposed as an alternative solution to the two important problems in communications, namely, effective / efficient / signal processing and secure encryption/decrypton. The whole system is able to both compress and encrypt data with attack immunity.

This paper focuses on examining a new type of n-additive maps called the symmetric reverse n-derivations. As implied by its name, it combines the ideas of n-additive maps and reverse derivations, with a 1-reverse derivation being the ordinary reverse derivation. We explore several findings that expand our knowledge of these maps, particularly their presence in semiprime rings and the way rings respond to specific functional identities involving elements of ideals. Also, we provide examples to help clarify the concept of symmetric reverse n-derivations. This study aims to deepen the understanding of these symmetric maps and their properties within mathematical structures.

This paper focuses on examining a new type of $n$-additive maps called the symmetric reverse $n$-derivations. As implied by its name, it combines the ideas of $n$-additive maps and reverse derivations, with a $1$-reverse derivation being the ordinary reverse derivation. We explore several findings that expand our knowledge of these maps, particularly their presence in semiprime rings and the way rings respond to specific functional identities involving elements of ideals. Also, we provide examples to help clarify the concept of symmetric reverse $n$-derivations. This study aims to deepen the understanding of these symmetric maps and their properties within mathematical structures.

A class of nearly Sasakian manifolds is considered. We discussion geometric effects of some symmetries on such manifolds, and show, under a certain condition, that the class of Ricci-symmetric nearly Sasakian manifolds is a subclass of Einstein manifolds. We prove that a nearly Sasakian space form with Ricci tensor satisfying the Codazzi equation is either a Sasakian manifold with a constant $\phi$-holomorphic sectional curvature $\mathcal{H}=1$ or a $5$-dimensional proper nearly Sasakian manifold with a constant $\phi$-holomorphic sectional curvature $\mathcal{H}>1$. We also prove that the spectrum of the operator $H^{2}$ generated by the nearly Sasakian manifold is a set of simple eigenvalue $0$ and an eigenvalue of multiplicity $4$. We show that there exist integrable distributions on the same manifolds with totally geodesic leaves, and prove that there are no proper nearly Sasakian space forms with constant sectional curvature.

Throughout this paper, we will establish a comprehensive theoretical foundation and rigorously develop the methodology to investigate the structure of quotient ring S/P under the influence of symmetric generalized n-derivations, where S represents an arbitrary ring, and P signifies a prime ideal of S satisfying certain algebraic identities acting on prime ideal P without relying on the assumption of primeness or semi-primeness of the ring.

In an $m$-person symmetric game, all players are identical and indistinguishable. In this paper, we find that the payoff tensor of the player $k$ in an $m$-person symmetric game is $k$-mode symmetric, and the payoff tensors of two different individuals are the transpose of each other. Furthermore, we reformulate the $m$-person symmetric game as a tensor complementary problem and demonstrate that locating a symmetric Nash equilibrium is equivalent to finding a solution to the resulting tensor complementary problem. Finally, we use the hyperplane projection algorithm to solve the resulting tensor complementary problem, and we present some numerical results to find the symmetric Nash equilibrium.

The orthogonal matrix with cube be symmetric is a common class of matrices with important properties. We pay attention to this kind of matrices. By using the close relationship between the eigenvalues of a matrix and the trace of its power, we obtain the algorithm for its all possible different eigenvalues and multiplicities. The calculation formula is expressed only by the trace of a matrix and its power, avoiding solving the characteristic polynomial. The method is simple and practical. Furthermore, a new essential characterization for the sum of orthogonal matrix pairs being orthogonal is given as well.

The Gol'denveizer problem of a torus can be described as follows: a toroidal shell is loaded under axial forces and the outer and inner equators are loaded with opposite balanced forces. Gol'denveizer pointed out that the membrane theory of shells is unable to predict deformation in this problem, as it yields diverging stress near the crowns. Although the problem has been studied by Audoly and Pomeau (2002) with the membrane theory of shells, the problem is still far from resolved within the framework of bending theory of shells. In this paper, the bending theory of shells is applied to formulate the Gol'denveizer problem of a torus. To overcome the computational difficulties of the governing complex-form ordinary differential equation (ODE), the complex-form ODE is converted into a real-form ODE system. Several numerical studies are carried out and verified by finite-element analysis. Investigations reveal that the deformation and stress of an elastic torus are sensitive to the radius ratio, and the Gol'denveizer problem of a torus can only be fully understood based on the bending theory of shells.

We present some exact analytical solutions describing, either the evolution of fluid distributions corresponding to a ghost star (vanishing total mass), or describing the evolution of fluid distributions which attain the ghost star status at some point of their lives. The first two solutions correspond to the former case, they admit a conformal Killing vector (CKV) and describe the adiabatic evolution of a ghost star. Other two solutions corresponding to the latter case are found, which describe evolving fluid sphere absorbing energy from the outside, leading to a vanishing total mass at some point of their evolution. In this case the fluid is assumed to be expansion–free. In all four solutions the condition of vanishing complexity factor was imposed. A discussion of the physical implications of the results, is presented.

We explore an idea put forward many years ago by Zeldovich and Novikov concerning the existence of compact objects endowed with arbitrarily small mass. The energy-density of such objects, which we call “Ghost stars”, is negative in some regions of the fluid distribution, producing a vanishing total mass. Thus, the interior is matched on the boundary surface to Minkowski space-time. Some exact analytical solutions are exhibited and their properties are analyzed. Observational data that could confirm or dismiss the existence of this kind of stellar object, is commented.

Background: Distal sensory polyneuropathy (DSP) and distal neuropathic pain (DNP) remain significant challenges for older people with HIV (PWH), necessitating enhanced clinical attention. HIV and certain antiretroviral therapies (ART) can compromise mitochondrial function and impact mitochondrial DNA (mtDNA) replication, which is linked to DSP in ART-treated PWH. Methods: This study investigated mtDNA, mt fission and fusion protein, and mt electron transport chain protein changes in the dorsal root ganglion (DRG) and sural nerve (SuN) from 11 autopsied PWH. In antemortem standardized assessments, six had no or one sign of DSP, while five exhibited two or more DSP signs. Digital droplet polymerase chain reaction (ddPCR) measured mtDNA quantity and the common deletion (CD) in isolated DNA. Results: We found lower mtDNA copy numbers in DSP+ donors. SuN exhibited a higher proportion of mtDNA CD than DRGs in both groups. Mitochondrial electron transport chain (ETC) proteins were altered in DRG of DSP+ compared to DSP- donors, particularly complex I. Conclusion: These findings suggest reduced mtDNA quantity and increased CD abundance may contribute to DSP in PWH, indicating diminished mitochondrial activity in sensory neurons. Accumulated ETC proteins in the DRG imply impaired mitochondrial transport to the sensory neuron's distal portion. Identifying molecules to safeguard mitochondrial integrity could aid in treating or preventing HIV-associated peripheral neuropathy.

Weak signal spectral detection is a serious problem in many applications, especially the target possesses certain frequency band and under low signal-to-noise ratio (SNR). A kind of novel technique based on pre-whitening scale-transformation symmetric bistable parallel stochastic resonance (SR) is proposed to solve the problem. Firstly, the pre-whitening can ensure the even distribution of the receiving signal to fit the requirement of SR processing. Secondly, the scale- transformation can help to utilize the weak signal improvement property especially under low frequency band more effectively. Thirdly, the symmetric bistable parallel SR can try to reduce the variance of the clutter and additive noise fluently. Fourthly, by subtracting the steady state re-sponse of the selected symmetric bistable SR system from the parallel SR output, the weak signal spectral detection objective can be realized successfully. Simulation results based on the real sea clutter radar data guarantee the effectiveness and applicability of the proposed symmetric bistable PSR processing approach.

This paper presents four novel schemes for secure data encryption utilizing mathematical transformations. The first scheme employs matrix manipulations and partitioning of numerical values derived from plain text characters, constructing a cipher through matrix additions. The second scheme introduces division operations and additional transformation layers for enhanced data obscurity. The third scheme incorporates tridiagonal matrices, creating a structured encryption process. The fourth scheme refines this approach with quotient-remainder operations and symmetric keys to construct a tridiagonal matrix cipher. Detailed algorithms for encryption and decryption are provided, with examples illustrating practical applications. This work contributes to mathematical cryptography by offering enhanced security methods for digital communication.

In this study, we provide the Lie symmetries and a classification of plane symmetric static space-times. Based on the invariance of the Lagrange equations of plane symmetries static space-time systems under the transformation Lie group, we provide the Lie symmetry determination equation, Lie symmetry theorem, and the conserved quantity of the systems; by utilizing the Lie symmetry method to solute the system, we give complete classification of the plane symmetric static space-times systems. The research results indicate that using the Lie symmetry method to study plane symmetric static spacetime can identify a series of conserved quantities that exist in the system; Discovered 5 basic Lie symmetries in the system; When the metric parameters of the system are appropriately selected, the plane symmetric static spacetime can have 6, 7, 8, 9, 11, and 17 Lie symmetric symmetries and conserved quantities.

The Einstein’s Boxes paradox was developed by Einstein, de Broglie, Heisenberg, and others to demonstrate the incompleteness of the Copenhagen Formulation of quantum mechanics. I explain the paradox using the Copenhagen Formulation. I then show how a Time-Symmetric Formulation of quantum mechanics resolves the paradox in the way envisioned by Einstein and de Broglie. Finally, I describe an experiment that can distinguish between these two formulations.

Diaminomaleonitrile (DAMN) is an electron-rich ligand which is commonly used in the synthesis of purines, amides and Schiff base ligands. In the last case lies the interest in this molecule, given its symmetry and apparent facility to form various ligands and complexes of interest in fields such as organic solar cells and catalysis among others. Nevertheless, its bisubstitution with aldehydes displays certain difficulty due to the double conjugated presence of the nitrile group (C≡N) in its structure, which significantly affect its coordination behavior by modulating the chemical reactivity of its amines. In addition to presenting a practical resume of guidelines for the preparation of different bisubstituted compounds from DAMN, this paper reviews the possibility of attaining a precise characterization by simple spectroscopic techniques. We provide an additional discussion for one of these techniques (commonly reported but often overlooked), given its potential to provide both the symmetry and E/Z configuration of the product. We hope the comprehensive evidence discussed and shown in this review will be helpful to further develop and understand the products derived of this interesting molecule in their broad applications.

Euler sums are alternating (or level two) extension of multiple zeta values (MZVs). Kaneko and Tsumura initiated the study of multiple T-values (MTVs), another level two generalization, by restricting the summation indices in the definition of MZVs to a fixed parity pattern. In this paper, we shall study finite MTVs and their alternating versions which are level two and level four variations of finite MZVs, respectively. We conjecture that all finite MZVs are in the Q-span of finite MTVs which in turn apparently lie in the span of finite Euler sums, and the inclusions are both proper. We shall first provide some structural results for Euler sums of small weights, guided by the author's previous conjecture that the finite Euler sum space of weight w is isomorphic to a quotient Euler sum space of weight w. Then, by utilizing some well-known properties of the classical alternating MTVs, we shall derive a few important Q-linear relations among the finite alternating MTVs, including the reversal, linear shuffle and sum relations. We then compute the upper bound for the dimension of the Q-span of weight w finite (alternating) MTVs for w<9, both rigorously using the newly discovered relations and numerically aided by computers.

In this article, authors introduce a new class of degenerate Hermite poly-Genocchi polynomials and give some identities of these polynomials related to the Stirling numbers of the second kind. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions. These results extend some known summations and identities of degenerate Hermite poly-Bernoulli numbers and polynomials studied by Khan [8].

The potential of metallic lithium to become the anode material for next-generation batteries is hampered by significant challenges, chief among which is dendrite growth during battery charging. These dendritic structures not only impair battery performance but also pose safety risks. Among the non-destructive analytical techniques in battery research, Magnetic Resonance Imaging (MRI) stands out as a promising tool. However, the direct imaging of lithium by 7Li MRI is hindered by its low sensitivity and spatial resolution, making its use for of dendritic growth imaging very difficult. Instead, a recently introduced indirect imaging approach based on 1H MRI of the electrolyte was used in this study. This method was used for sequential 3D imaging to monitor the charging process of lithium metal symmetric cells in three different electrical circuits: single cell, four cells in parallel, four cells in series. The measured sequential images allowed measurement of dendrite growth in each cell using volumetric analysis. The growth results confirmed the theoretical expectation that growth across cells is uneven in a parallel circuit and even in a series circuit. The methods presented in this study can be applied also to many other dendrite-related issues in batteries.

This article explores matter collineations (MCs) of static plane-symmetric spacetimes, considering the stress-energy tensor in its contravariant and mixed forms. We solve the MC equations in two cases: when the energy-momentum tensor is nondegenerate and degenerate. For the case of degenerate energy-momentum tensor, we employ a direct integration technique to solve the MC equations, which leads to an infinite-dimensional Lie algebra. On the other hand, when considering the nondegenerate energy-momentum tensor, the contravariant form results in a finite-dimensional Lie algebra with dimensions of either 4 or 10. However, in the case of the mixed form of the energy-momentum tensor, the dimension of the Lie algebra is infinite. Moreover, the obtained MCs are compared with those already found for covariant stress-energy.

In this paper, we represent the generating function of w-torsion Fubini polynomials by fermionic p-adic integral on Z_p. Then we consider a quotient of such fermionic p-adic integrals on Z_p, representing generating functions of three w-torsion Fubini polynomials and derive some new symmetric identities for the w-torsion Fubini and two variable w-torsion Fubini polynomials.

Integration of multi-view datasets which are comprised of heterogeneous sources or different representations is challenging to understand the subtle and complex relationship in data. Such data integration methods attempt to combine efficiently the complementary information of multiple data types to construct a comprehensive view of underlying data. Nonnegative matrix factorization (NMF), an approach that can be used for signal compression and noise reduction, has aroused widespread attention in the last two decades. The Kullback–Leibler divergence (or relative entropy) information distance can be used to measure the loss function of NMF. In this article, we propose a fast and robust framework (RSNMF) based on symmetric nonnegative matrix factorization (SNMF) and similarity network fusion (SNF) for clustering human microbiome data including functional, metabolic and phylogenetic profiles. Many existing methods typically utilize all the information provided by each view to create a consensus representation, which often suffers a lot from noise in data and cannot provide a precise representation of the latent data structures. In contrast, RSNMF combines the strength of SNMF and the advantage of SNF to form a robust clustering indicator matrix thus can reduce the noise influence. We conduct experiments on one synthetic and two real dataset (microbiome data, text data) and the results show that the proposed RSNMF has better performance over the baseline and the state-of-art methods, which demonstrates the potential application of RSNMF for microbiome data analysis.

In this paper, we define the cohomology of a modified $\lambda$-differential left-symmetric algebra with coefficients in a suitable representation. We also introduce the notion of modified $\lambda$-differential left-symmetric 2-algebra. We classify linear deformations and abelian extensions of modified $\lambda$-differential left-symmetric algebras using the second cohomology group and classify skeletal modified $\lambda$-differential left-symmetric 2-algebra using the third cohomology group as our propose cohomology applications. Moreover, we prove that strict modified $\lambda$-differential left-symmetric 2-algebras are equivalent to crossed modules of modified $\lambda$-differential left-symmetric algebras.

In this paper, under the symmetric entropy and the scale squared error loss functions, we consider the maximum likelihood (ML) estimation and Bayesian estimation of the Shannon entropy and Rényi entropy of the two-parameter inverse Weibull distribution. In the ML estimation, the dichotomy is used to solve likelihood equation. In addition, the approximation confidence interval is given by the Delta method. Because the form of estimation results is more complex in the Bayesian estimation, the Lindley approximation method is used to achieve the numerical calculation. Finally, Monte Carlo simulations and a real data set are used to illustrate the results derived. By comparing the mean square error between the estimated value and the real value, it can be found that the performance of ML estimation of Shannon entropy is better than that of Bayesian estimation, and there is no significant difference between the performance of ML estimation of Rényi entropy and that of Bayesian estimation.

New series of compounds containing both heterocycle moieties and pseudo-symmetric hydroxyethylamine core were obtained using a simple synthetic path that can provide a library of compounds in few steps and high yields. Furthermore, diversity-oriented synthesis was studied to change different functionalities according to needs. The in vitro inhibition activity against recombinant HIV-1 protease was evaluated. A beneficial effect of this class of compounds can be obtained either for the presence of a bis-benzyl group into the core and for the heterocyclic moiety in P1, specifically the indole ring. Docking analysis was also reported.

In this paper, we introduce a new class of Hermite-Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we derive symmetric identities of Hermite-Fubini numbers and polynomials by using generating functions.

The fitting and modeling of skewed, complex, symmetric, and asymmetric datasets is an exciting research topic in many fields of applied sciences, notably lifetime, medical, and financial sciences. The Heavy tailed Nadarajah Haghighi model is introduced by compounding the heavy tailed family and Nadarajah Haghighi distribution in this paper. The so obtained model has three parameters accounting for the scale and shape of the distribution. The proposed distribution's fundamental characteristics such as probability density, cumulative distribution, hazard rate, and survival functions are provided, and several key statistical properties are established, and several entropy information measures are proposed. The estimation of model parameter is performed via the ML procedure. Further, different simulation experiments are conducted to demonstrate the performance of proposed estimator’s using some measure, like the average estimate, the average bias, and associated mean square error. Finally, we are applied our proposed model to analyze three different real datasets. In our illustration, we are compared the practicality of the recommended model with several well-known competing models.

Background: One of the most astounding discoveries of recent times is the recognition that cancer embodies a transition from a higher level of metazoan cell organization to a more foundational pre-metazoic state. This shift is steered by genes housed within the ancestral genome compartment, pervasive across all metazoan genomes, encompassing humans, and governed by a pre-metazoic gene regulatory mechanism (aGRN). This work aims to highlight the emerging field of evolutionary cancer cell biology (ECCB), which points to the deep homology between cancer and protist life cycles tracing back to the common ancestor of amoebozoans, metazoans, and fungi (AMF). The ECCB analysis reveals the essence of the non-gametogenic germline of the AMF ancestor, which serves as a blueprint for all metazoan germlines and stem cell lineages and controls the life cycle of cancer. Every germ and stem cell lineage of humans and metazoans traces its lineage back to this Urgermline, transmitting crucial processes such as asymmetric cell cycling, differentiation, stemness, and phenomena like GST and SGT (aka EMT and MET) to their subsequent evolutionary descendants. Oxygen-sensitive germline and stem cells suffer DNA-DSB due to stress and oxygen ranges reminiscent of ancestral hyperoxia, leading to cell senescence. Cells that can overcome senescence can proliferate as DSCD cells with defective symmetric cell division, paving the way for malignancy and PGCC cancers. Conclusions: Understanding cancer from its evolutionary origins may help break some of the logjams in cancer prevention and open up new therapeutic pathways.

We establish a new Gagliardo-Nirenberg inequality characterized by radial symmetry and involving potentials exhibiting pure power polynomial behaviour. As an application of our result, we investigate the existence of extremals for this inequality, which also correspond to stationary solutions for the nonlinear Schrödinger equation with inhomogeneous nonlinearity, competing with Hs-subcritical nonlinearities, either of local or non-local nature.

Gradient based methods are popularly used in training neural networks and can be broadly categorized into first and second order methods. Second order methods have shown to have better convergence compared to first order methods, especially in solving highly nonlinear problems. The BFGS quasi-Newton method is the most commonly studied second order method for neural network training. Recent methods have shown to speed up the convergence of the BFGS method using the Nesterov’s acclerated gradient and momentum terms. The SR1 quasi-Newton method though less commonly used in training neural networks, are known to have interesting properties and provide good Hessian approximations when used with a trust-region approach. Thus, this paper aims to investigate accelerating the Symmetric Rank-1 (SR1) quasi-Newton method with the Nesterov’s gradient for training neural networks and briefly discuss its convergence. The performance of the proposed method is evaluated on a function approximation and image classification problem.

The Einstein’s Boxes paradox was developed by Einstein, de Broglie, Heisenberg, and others to demonstrate the incompleteness of the Copenhagen Formulation of quantum mechanics. I explain the paradox using the Copenhagen Formulation. I then show how a Time-Symmetric Formulation of quantum mechanics resolves the paradox in the way envisioned by Einstein and de Broglie. Finally, I describe an experiment that can distinguish between these two formulations.

In the paper we consider conformal mappings of Riemannian spaces onto Ricci-2-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-2-symmetric spaces. The main equations for the mappings are obtained as a closed system of differential equations of Cauchy-type in covariant derivatives. We have found the number of essential parameters which the solution of the system depends on. Similar approach was applied for the case of conformal mappings of Riemannian spaces onto Ricci-m-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-m-symmetric spaces.

In this paper, we introduce a new class of Laguerre-based Hermite-Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we derive symmetric identities of Laguerre-based Hermite-Fubini numbers and polynomials by using generating functions.

Information-related measures are useful tools for multi-variable data analysis, as measures of dependence among variables, and as descriptions of order and disorder in biological and physical systems. Measures, like marginal entropies, mutual / interaction / multi -information, have long been used in a number of fields including descriptions of systems complexity and biological data analysis. The mathematical relationships among these measures are therefore of significant inherent interest. Relations between common information measures include the duality relations based on Möbius inversion on lattices. These are the direct consequence of the symmetries of the lattices of the sets of variables (subsets ordered by inclusion). While these relationships are of significant interest there has been, to our knowledge, no systematic examination of the full range of relationships of this diverse range of functions into a unifying formalism as we do here. In this paper we define operators on functions on these lattices based on the Möbius inversions that map functions into one another (Möbius operators). We show that these operators form a simple group isomorphic to the symmetric group S₃. Relations among the set of functions on the lattice are transparently expressed in terms of the operator algebra, and, applied to the information measures, can be used to derive a wide range of relationships among diverse information measures. The Möbius operator algebra is naturally generalized which yields extensive new relationships. This formalism now provides a fundamental unification of information-related measures, and the isomorphism of all distributive lattices with the subset lattice implies an even broader application of these results.

We introduce a new kind of extended Hermite-based Frobenius type Eulerian polynomials and then derive diverse explicit and implicit summation equations including some symmetric formulas by utilizing series manupulation method. Multifarious summation formulas and identities given earlier for some well known polynomials such as Eulerian polynomials and Frobenius type Eulerian polynomials are generalized.

In this paper, we introduce a general family of Lagrange-based Apostol-type Hermite polynomials thereby unifying the Lagrange-based Apostol Hermite-Bernoulli and the Lagrange-based Apostol Hermite-Genocchi polynomials. We also define Lagrange-based Apostol Hermite-Euler polynomials via the generating function. In terms of these generalizations, we find new and useful relations between the unified family and the Apostol Hermite-Euler polynomials. We also derive their explicit representations and list some basic properties of each of them. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions.

Titania is one of the most comprehensively studied nanostructures due to its widespread applications in production of catalytic, gas- sensing and corrosion- resistance materials [1]. M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices which are numerical parameters capturing structural and chemical properties. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules are correlated with their structure like boiling point, stability, strain energy etc of chemical compounds. In this paper, we determine M-polynomials of single-walled titanium (SW TiO2) nanotubes and recover important topological degree based indices of them to theoretically judge these nanotubes. We also use Maple to plot surfaces associated to different types of single-walled titanium (SW TiO2) nanotubes.

Polarimetric features extracted from polarimetric synthetic aperture radar (PolSAR) images contain abundant scattering information of objects. Utilizing this information for PolSAR image classification can improve accuracy and enhance object monitoring. Although significant progress has been achieved in related research, there are still issues such as insufficient utilization of polarimetric information and features. In this paper, a deep learning classification method based on polarimetric channel power features for PolSAR is proposed. The distinctive characteristic of this method is that the polarimetric features inputted into the deep learning network are the power values of polarimetric channels, where these channels are treated equivalently and contain complete polarimetric information. In terms of experimental comparative study, besides polarimetric power combinations, three different data input schemes were employed as data for the input end of the convolutional neural network (CNN), taking into account existing research. The neural networks utilizes the extracted polarimetric features to classify images, and the classification accuracy analysis is employed to compare the strengths and weaknesses of different input schemes. It is worth mentioning that the polarized characteristics of the data input scheme mentioned in this article have been derived through rigorous mathematical deduction, and each polarimetric feature has clear physical meaning. By testing different data input schemes on the Gaofen-3 (GF-3) PolSAR image, the experimental results show that the method proposed in this article outperforms existing methods and can improve the accuracy of classification to a certain extent, validating the effectiveness of this method in large-scale area classification.

In this paper we investigate analytic automorphisms of complex topological vector spaces and their applications to linear and nonlinear transitive operators. We constructed some examples of polynomial automorphisms which show that a natural analogue of the Jacobian Conjecture for infinite dimensional spaces is not true. Also, we prove that any separable Fréchet space supports a transitive analytic operator which is not a polynomial. We found some connections of analytic automorphisms and algebraic bases of symmetric polynomials and applications to hypercyclisity of composition operators.

A number of experimental and numerical studies point out that incorporating a rotating cylinder can superiorly enhance the aerofoil performance, especially for higher velocity ratios. Yet, there have been less or no studies exploring the effects of lower velocity ratio at a higher Reynolds number. In the present study, we investigated the effects of Moving Surface Boundary-layer Control (MSBC) at lower velocity ratios (i.e. cylinder tangential velocity to free stream velocity) and higher Reynolds number on a symmetric aerofoil (e.g. NACA 0021) and an asymmetric aerofoil (e.g. NACA 23018). In particular, the aerodynamic performance with and without rotating cylinder at the leading edge of the NACA 0021 and NACA 23018 aerofoil was studied on the wind tunnel installed at Aerodynamics Laboratory. The aerofoil section was tested in the low subsonic wind tunnel, and the lift coefficient and the drag coefficient were studied for different angles of attack. The experiments were conducted for two Reynolds numbers: 200000 and 250000 corresponding to two free stream velocities: 20 m/s and 25 m/s, respectively, for six different angle of attacks (-5°, 0°, 5°, 10°, 15° and 20°). This study demonstrates that the incorporation of a leading edge rotating cylinder results in an increase of lift coefficient at lower angle of attacks (maximum around 33%) and delay in stall angle (from 10° to 15°) relative to the aerofoil without rotating cylinder.

There is an increasing interest in biomarkers of nitric oxide dysregulation and oxidative stress to guide management and identify new therapeutic targets in patients with chronic obstructive pulmonary disease (COPD). We conducted a systematic review and meta-analysis of the association between circulating metabolites within the arginine (arginine, citrulline, ornithine, asymmetric, ADMA, and symmetric, SDMA dimethylarginine), transsulfuration (methionine, homocysteine, and cysteine) and folic acid (folic acid, vitamin B6, and vitamin B12) metabolic pathways and COPD. We searched electronic databases from inception to 30 June 2023 and assessed the risk of bias and the certainty of evidence. In 21 eligible studies, compared to healthy controls, patients with stable COPD had significantly lower methionine (standardized mean difference, SMD=-0.50, 95% CI -0.95 to -0.05, p=0.029) and folic acid (SMD=-0.37, 95% CI -0.65 to -0.09, p=0.009), and higher homocysteine (SMD=0.78, 95% CI 0.48 to 1.07, p˂0.001) and cysteine concentrations (SMD=0.34, 95% CI 0.02 to 0.66, p=0.038). Additionally, COPD was associated with significantly higher ADMA (SMD=1.27, 95% CI 0.08 to 2.46, p=0.037), SDMA (SMD=3.94, 95% CI 0.79 to 7.08, p=0.014), and ornithine concentrations (SMD=0.67, 95% CI 0.13 to 1.22, p=0.015). In subgroup analysis, the SMD of homocysteine was significantly associated with the biological matrix assessed and the forced expiratory volume in the first second to forced vital capacity ratio, but not with age, study location, or analytical method used. Our study suggests the presence of significant alterations in metabolites within the arginine, transsulfuration, and folic acid pathways which can be useful for assessing nitric oxide dysregulation and oxidative stress and identifying novel treatment targets in COPD. (PROSPERO registration number: CRD42023448036)

Starting from Thomas Friedrich’s work “Weak Spin(9) structures on 16-dimensional Riemannian manifolds”, we review several interactions between Spin(9) and geometries related to octonions. Several topics are discussed in this respect: explicit descriptions of the Spin(9) canonical 8-form and its analogies with quaternionic geometry, the role of Spin(9) both in the classical problems of vector fields on spheres and in the geometry of the octonionic Hopf fibration. Next, we deal with locally conformally parallel Spin(9) manifolds in the framework of intrinsic torsion. Finally, we discuss applications of Clifford systems and Clifford structures to Cayley-Rosenfeld planes and to three series of Grassmannians.

Spin-orbit coupling and nonparaxiality effects during propagation of vortex vector light beams in a cylindrical graded-index waveguide are investigated by solving the full three-component field Maxwell’s equations. Symmetry breaking effects for left- and right-handed circularly polarized vortex light beams propagating in a rotationally symmetric graded-index optical fiber are considered. The mode-group delay in a graded-index fiber due to spin-orbit interaction is demonstrated. It is shown that the relative delay times between vortex pulses of opposite circular polarizations of the order of 10 ps/km can be observed in graded-index fibers for high-order topological charges.

As the embedded device and internet of things (IoTs) concept prevalent in today's world, there is an increasing demand for the security and performance requirements on deploying these devices to private and public sectors. The crucial part of it is to protect privacy, confidentiality and integrity, meanwhile, maintain an adequate level of performance during transmission, storage and access of critical information. While the conventional cryptography methods, such as the Advanced Encryption Standard (AES), SHA$-$2 hashing method and RSA and Diffie Hellman for message authentication and identification, work well on systems which have reasonable processing power and memory capabilities. These do not scale well into a world with embedded systems and sensor networks, in conjunction with their nature of smaller size and lower cost. Thus, in the context of resource constrained device, lightweight cryptography methods are proposed to overcome many of the problems of conventional cryptography possessed. This includes constraints related to physical size, processing requirement, memory limitation, energy drain and production cost. This paper provides a survey of the architectures that are defined as replacements for conventional ciphers within an IoTs space and discuss some trends in the design of future lightweight algorithms. The performance metrics are carefully chosen to reflect and assess the suitability for embedded devices. The aim of this research is to identify the various performance metrics applied on different types of symmetric block ciphers especially lightweight ciphers and compare the results on versatile platforms with stream ciphers and public key methods. The comparative analysis on efficient LW cipher will be tested against other similar block ciphers on both MacBook Pro with Intel core and resource constrained device Raspberry Pi with ARM processor.

The Sine-Gordon expansion method is implemented to construct exact solutions some conformable time fractional equations in Regularized Long Wave(RLW)-class. Compatible wave transform reduces the governing equation to classical ordinary differential equation. The homogeneous balance procedure gives the order of the predicted polynomial-type solution that is inspired from well-known Sine-Gordon equation. The substitution of this solution follows the previous step. Equating the coefficients of the powers of predicted solution leads a system of algebraic equations. The solution of resultant system for coefficients gives the necessary relations among the parameters and the coefficients to be able construct the solutions. Some solutions are simulated for some particular choices of parameters.

This study employs the reflection symmetry decomposition (RSD) method to extract polarization scattering features from ground object images, aiming to determine the optimal data input scheme for deep learning networks in polarimetric synthetic aperture radar classification. Eight distinct polarizing feature combinations are designed, and the classification accuracy of various approaches is evaluated using the classic convolutional neural networks(CNNs) AlexNet and VGG16. The findings reveal that the commonly employed 6-parameter input scheme, favored by many researchers, lacks the comprehensive utilization of polarization information and warrants attention. Intriguingly, leveraging the complete 9-parameter input scheme based on the polarization coherence matrix results in improved classification accuracy. Furthermore, the input scheme incorporating all 21 parameters from the RSD and polarization coherence matrix notably enhances overall accuracy and the Kappa coefficient compared to the other 7 schemes. This comprehensive approach maximizes the utilization of polarization scattering information from ground objects, emerging as the most effective CNN input data scheme in this study. Additionally, the classification performance using the second and third component total power values (P2 and P3) from the RSD surpasses the approach utilizing surface scattering power value (PS) and secondary scattering power value (PD) from the same decomposition.

Space-time evolution is briefly explained by using the 3-dimensional quantized space model (TQSM) based on the 4-dimensional (4-D) Euclidean space. The energy (mass), charges and absolute time are newly defined based on the 4-D Euclidean space. The photons and gravitons are understood as the 2-D space fluctuations along the space axes and 1-D time fluctuations along the time axis, respectively. This indicates that the electromagnetic (EM) and gravitational (G) waves can be unified into the so called gravityelectromagnetic (GEM) wave which has both space and time fluctuations. The photon with zero force fields is the 2EM wave because an EM wave corresponds to a charged fermion. The dark matter bosons, weak force bosons, strong force bosons are the 1-D time fluctuations which can be expressed by the G waves. This indicates that all five forces are unified by the GEM wave. It is called as the super unification theory in the present work. And the force carrying bosons and mesons are, for the first time, proposed as the possible candidates of the magnetic monopoles like the fermions and baryons are the electric monopoles. The signs of the magnetic charges quantized as q_m=cq are newly defined. The big bang is understood by the space-time evolution of the 4-D Euclidean space but not by the sudden 4-D Minkowski space-time creation. The big bang process created the matter universe with the positive energy and the partner anti-matter universe with the negative energy from the CPT symmetry.

This paper proposes a method of extracting energy from zero-point energy and evaluates the amount of energy gained. In addition, this electric circuit-based approach exhibits the Meissner effect, suggesting a new type of superconductivity that does not require refrigeration. The proposed method can provide extremely large amounts of energy, which is more than a conventional power station, without consuming fossil fuels or emitting radiation. Thus, it has the potential to solve the global energy problem. It involves preparing two electric loops containing diodes and connecting the loops together with current sources. The diodes are oriented in the same direction within each loop but in opposite directions in different loops. With this setup, the currents from the current sources build iteratively within the loops, resulting in large output currents. Our numerical analysis indicates that extremely large electric potentials are produced, which in turn yield large output currents. In addition, we confirm numerically that the voltage is zero around a loop and show analytically that the Meissner effect is present, proving the existence of a new type of superconductivity. Furthermore, when we introduce induction coils to not break the loop’s symmetry, they store extremely large amounts of energy and we can thus obtain energy from them via discharge currents.

Diabetes mellitus is the global epidemic of the 21st century affecting millions worldwide. Usually, patients with long-standing type one diabetes (T1D) or type two diabetes (T2D) tend to develop complications. A common complication is the degenerative of the nerves in the peripheral nervous system (PNS). This complication is known as distal symmetric polyneuropathy or just diabetic neuropathy. A variety of symptoms can be experienced with this complication, including pain and numbness. One characterization of this complication is the sensory loss that begins in the lower extremities and spreads substantially to the fingers and hand. There is no clear mechanism for how this happens in diabetic patients. Studies have shown that nerve damage from this complication can be due to oxidative stress, sorbitol accumulation, and advanced glycation end products (AGEs). Some of the most common medications being provided for diabetic neuropathic pain (DNP) include amitriptyline and desipramine. Other medications also include gabapentin and duloxetine. There are noninvasive options, such as acupuncture, that could provide beneficial data if rigorous studies are conducted. A number of new studies are being completed to identify more effective treatments for this condition.

This paper reports an experimental investigation on compression after low-velocity impact response for two lay-up configurations of symmetric CFRP laminated composite specimens obtained by reversing their angle-ply orientation, namely [0/-45/45/90]s versus [90/45/-45/0]s, the impact velocity of the projectile up to the BVID level being subsequently considered. To this aim, a modified Compression-After-Impact (CAI) test device is proposed that involves clamping the specimen's upper and lower edges between two adjustable wide and flat anti-buckling plates through a removable bolt-nut assembly. Such a solution relies on the fact that the specimen's active length is shortened, reducing the risk of global buckling. Besides, the bolts carry part of the load with minor localized bearing damage, provided that the metallic plates act as washers by supporting the bolt-bearing region laterally, thus avoiding crashing failures at the specimens’ loaded edges. With these settings, roughly the same percent decrease in the average values of maximum compression load (i.e., 22%) was recorded for both lay-up configurations impacted up to their BVID threshold, whereas in terms of compressive stiffness behavior, a reduction of 17 % was found for [0/-45/45/90]s specimens compared to 6 % obtained for [90/45/-45/0]s specimens.

Cancer is a complex and devastating disease that has engaged scientists and researchers for decades. Despite tremendous efforts, previous hypotheses about cancer development have not achieved significant breakthroughs. Evolutionary Cancer Cell Biology (ECCB) is a novel and emerging branch of oncological science that provides an evolutionary perspective on the origin of cancer. It reveals that the cancer genome evolved hundreds of millions of years ago, long before multicellular organisms such as metazoans and humans emerged. ECCB aims to unify all evolutionary insights, hypotheses, and theories into a cohesive framework. It investigates the intricate relationship between cancer genomics and ancient pre-metazoan genes that emerge when normal cells transform into cancer cells. It challenges the conventional wisdom of cancer research by suggesting that cancer could arise through intrinsic cellular mechanisms without genetic alterations and mutations. Furthermore, it postulates that somatic mutations are only secondary, downstream events in the process of oncogenesis.