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This article describes a new method for evaluation of radial crush strength of paper cores. Based on the theory of multilayered composites, a mathematical model has been developed to calculate the value of destructive force during radial crushing of spirally shaped paper cores whose layers are made of different materials. To start calculations, it is necessary to have geometry parameters of the cores, Young's modulus and SCT of an individual component layers. [ABSTRACT FROM AUTHOR]

In this two-paper series, we prove the invariance of the Gibbs measure for a threedimensional wave equation with a Hartree nonlinearity. The novelty lies in the singularity of the Gibbs measure with respect to the Gaussian free field. In this paper, we focus on the dynamical aspects of our main result. The local theory is based on a paracontrolled approach, which combines ingredients from dispersive equations, harmonic analysis, and random matrix theory. The main contribution, however, lies in the global theory. We develop a new globalization argument, which addresses the singularity of the Gibbs measure and its consequences. [ABSTRACT FROM AUTHOR]

For decades, historians have debated the origins of Einstein's special theory of relativity. The derivation of the Lorentz Transformations given by Einstein in 1905 is studied in detail; and it is found to be mathematically inconsistent, and thus in error. Therefore, he must have been aware of the transformations at the time of writing the paper, which is an extremely minority opinion in the general literature. His attempt to rederive them starting from the synchronization condition is incorrect. Though the derivation is flawed, it does not affect many of the concepts he put forth that flow from the Lorentz Transformations. The observations given here will help resolve a long-standing dispute over the priority of the discovery of various parts of the theory. The priority, which is presently concentrated with Einstein, may need to be redistributed between Einstein, Lorentz, Poincare', Larmor, Voigt, and others. [ABSTRACT FROM AUTHOR]

Immediately following the commentary below, this previously published article is reprinted in its entirety: Cathleen Synge Morawetz, "The mathematical approach to the sonic barrier". [ABSTRACT FROM AUTHOR]

This article is intended to indicate and discuss some errors in N. Lavi’s paper “A Ganzstellensatz for semi-algebraic sets and a boundedness criterion for rational functions”. [ABSTRACT FROM AUTHOR]

The present comment concerns the correct presentation of an algorithm proposed in the above paper for the glow-curve deconvolution in the case of continuous distribution of trapping states. Since most researchers would use directly the proposed algorithm as published, they should be notified of its correct formulation during the fitting of TL glow curves of materials with continuous trap distribution using this Equation. [ABSTRACT FROM AUTHOR]

Object detection is one of the core tasks of computer vision, and bounding box (bbox) regression is one of the basic tasks of object detection. In recent years of related research, bbox regression is often used in the Intersection over Union (IoU) loss and its improved version. In this paper, for the first time, we introduce the Dice coefficient into the regression loss calculation and propose a new measure which is superior to and can replace the IoU. We define three properties of the new measure and prove the theory by mathematical reasoning and analysis of the existing work. This paper also proposes the N-IoU regression loss family. And the superiority of the N-IoU regression loss family is proved by designing simulation experiments and comparative experiments. The main results of this paper are: (1) The proposed new measure is better than IoU which can be used to evaluate bounding box regression, and the three properties of the new measure can be used as a broad criterion for the design of regression loss functions; and (2) we propose N-IoU loss. The parameter n of N-IOU can be debugged, which can be widely adapted to different application scenarios with higher flexibility, and the regression performance is better. [ABSTRACT FROM AUTHOR]

Variable (feature) selection plays an important role in data analysis and mathematical modeling. This paper aims to address the significant lack of formal evaluation benchmarks for feature selection algorithms (FSAs). To evaluate FSAs effectively, controlled environments are required, and the use of synthetic datasets offers significant advantages. We introduce a set of ten synthetically generated datasets with known relevance, redundancy, and irrelevance of features, derived from various mathematical, logical, and geometric sources. Additionally, eight FSAs are evaluated on these datasets based on their relevance and novelty. The paper first introduces the datasets and then provides a comprehensive experimental analysis of the performance of the selected FSAs on these datasets including testing the FSAs' resilience on two types of induced data noise. The analysis has guided the grouping of the generated datasets into four groups of data complexity. Lastly, we provide public access to the generated datasets to facilitate bench-marking of new feature selection algorithms in the field via our Github repository. The contributions of this paper aim to foster the development of novel feature selection algorithms and advance their study. [ABSTRACT FROM AUTHOR]

The charging coil plays an important role in the wireless charging system system. However, there are still some problems in the design of the wireless charging coil, such as the low coupling coefficient. In order to improve the coupling effect, this paper proposes an optimized design scheme for the metal shielding layer structure of DD coil. Firstly, the influence of the structure size of DD coil metal plate on the coupling coefficient is studied by the mathematical modeling analysis. Futhermore, the maxwell simulation is used to study the metal plate coupling coefficients with varying structure sizes, addressing receiving uniformity issues. The optimal size of the shielding layer is designed for optimal magnetic coupling in wireless charging. Finally, this paper validates the feasibility of the improved metal shielding layer through experiments. The research in this paper may have a reference role in the wireless charging system of electric vehicles. [ABSTRACT FROM AUTHOR]

In this paper, we study the well-posedness, ill-posedness and uniqueness of the stationary 3-D radial solution to the bipolar isothermal hydrodynamic model for semiconductors. The density of electron is imposed with sonic boundary and interiorly subsonic case and the density of hole is fully subsonic case. It is difficult to estimate the upper and lower bounds of the holes due to the coupling of electrons and holes and the degeneracy of electrons at the boundary. Thus, we use the topological degree method to prove the well-posedness of solution. We prove the ill-posedness of subsonic solution under some conditions by direct mathematical analysis and contradiction method. The ill-posedness property shows significant difference to the unipolar model. Another highlight of this paper is the application of specific energy method to obtain the uniqueness of solution in two cases. One case is the relaxation time τ = ∞ , namely, the pure Euler-Poisson case; the other case is j τ ≪ 1 , which means that, when the current flow is sufficiently small and the relaxation time is sufficiently large both can satisfy. [ABSTRACT FROM AUTHOR]

A unique photonic technique has been suggested and explained for different types of waveform generation, the proposed technique employs double LiNbO3 Mach–Zehnder single drive cascading modulators for pulse shaping and responsive modulators for polarization. By ordering the incident light polarized states it can produce accordingly dual distinct Spectra on two components of orthogonal polarization. The desired waveform would be obtained by detecting the photocurrents from the photodetector. This paper describes the complete mathematical analysis of polarization dependent cascade Mach–Zehnder modulators to generate a variety of microwave forms. Comprehensive mathematical analyses including simulations have been presented, and therefore we have successfully developed as well as generated delta waveform, half-wave rectifier waveform, full-wave rectifier waveform, and square wave types waveform. At the end of the paper experimental analysis has been done for the proof of concept purpose while the experimental results of a variety of microwave waveforms are compared with theoretical ones. There are good agreements between theoretical results with experimental ones. [ABSTRACT FROM AUTHOR]

The article discusses the result of an experimental study which shows that people do not follow the optimal strategy in practice and suggests two strategies for defeating human opponents in rock-paper-scissors (RPS). The study found that the probability of repeating a game on the next trial is well above one-third, while the strategy of always playing the symbol is assessed to be an effective strategy in defeating the symbol that the other player has previously played. The study also observed that the wins of each competition have increased by 26.4%, while the losses are decreased by 9.51%.

In this short paper, we look into a conclusion drawn by Alzalg (J Optim Theory Appl 169:32-49, 2016). We think the conclusion drawn in the paper is incorrect by pointing out three things. First, we provide a counterexample that the proposed inner product does not satisfy bilinearity. Secondly, we offer an argument why a pth-order cone cannot be self-dual under any reasonable inner product structure on $$\mathbb {R}^n$$ . Thirdly, even under the assumption that all elements operator commute, the inner product becomes an official inner product and the arbitrary-order cone can be shown as a symmetric cone, we think this condition is still unreasonable and very stringent so that the result can only be applied to very few cases. [ABSTRACT FROM AUTHOR]

Ahmad et al. (2015) consider a Transmuted Kumaraswamy distribution and study certain properties of their distribution. In the title of their paper they mention characterization of this distribution, but no characterizations are presented in the paper. In the present short note we establish certain characterizations of the Transmuted Kumaraswamy in three directions. [ABSTRACT FROM AUTHOR]

The use of the efficient score statistic in sequential monitoring procedures is reviewed and analysed. Various models that arise in applications are considered. The efficient score vector has the same optimality property as the generalized likelihood ratio, but it has a simple-structure requiring fewer estimations, and this is especially important when the data have a complicated structure. Furthermore, with the efficient score vector it is possible to detect which component of the parameter vector is different from the hypothetical or the historical value. The problems we solve here were the subjects of separate publications, but with the new methodology they are easily calculated examples. [ABSTRACT FROM AUTHOR]

This article introduces a team-based model of researchers in a specialty and investigates the manifestation of such teams in a specialty's literature. The proposed qualitative behavioral model, with its mathematical expression as a growth model, is significant because it simultaneously describes the two phenomena of collaboration and author productivity (Lotka's law) in a specialty. The model is nested: A team process models the creation of research teams and the success-breeds-success process of their production of articles, while at a lower level the productivity of authors within teams is also modeled as a success-breeds-success process. Interteam collaboration (weak ties) is modeled as random events. This simple growth model is shown to faithfully mimic six network metrics of bipartite article-author networks. The model is demonstrated on three example article collections from specialties that have a wide range of degree of collaboration: (a) a distance education collection with low collaboration degree, (b) a complex networks collection with typical collaboration degree, and (c) an atrial ablation collection with heavy collaboration degree. [ABSTRACT FROM AUTHOR]

In this short paper we show that the results obtained by [N. Hussain, V. Parvaneh, B. Samet and C. Vetro, Some fixed point theorems for generalized contractive mappings in complete metric spaces, Fixed Point Theory and Applications (2015) 2015:185] can be obtained without the continuity assumption for the self mapping. [ABSTRACT FROM AUTHOR]

• Mathematical and physical analyses of the introduced problem. • Reporting a serious error in an important dimensionless parameter. • Indicating that the reported numerical results are completely erroneous. This is a comment on the paper [Optics and Laser Technology 128 (2020) 106233; https://doi.org/10.1016/j.optlastec.2020.106233 ] titled "Exact coupled solution for photothermal semiconducting beams using a refined multi-phase-lag theory". Herein, we report a serious error in an important dimensionless parameter employed in the problem, revealing that the defined parameter is dimensional and wrong. Accordingly, all given numerical results are based on this serious mistake, and are completely erroneous. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the asymptotic behavior of a modified chemostat model. We first demonstrate the existence of equilibria. Then, we present a mathematical analysis for the model, the invariance, the positivity, the persistence of the solutions, and the asymptotic global stability of the interior equilibrium. Some numerical simulations are carried out to illustrate the main results. [ABSTRACT FROM AUTHOR]

Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections, and mappings. Projective geometry identifies a line with a single point, like the perspective on the horizon line and, due to this fact, it requires a restructuring of the real mathematical and numerical analysis. In particular, the problem of interpolating data must be refocused. In this paper, we define a linear structure along with a metric on a projective space, and prove that the space thus constructed is complete. Then, we consider an iterated function system giving rise to a fractal interpolation function of a set of data. [ABSTRACT FROM AUTHOR]

Summary: Optical millimeter‐wave generation is a predominant approach for the generation of high‐quality carrier signals for future wireless transmissions. This paper proposes an optical frequency 12‐tupling millimeter‐wave generation scheme using three cascaded‐MZMs assisted by polarization multiplexing for carrier suppression. A three‐stage MZM architecture produces the desired sixth‐order sidebands along with the undesired carrier signal. The proper adjustment of polarization direction and angle of polarization rotation lead to the effective suppression of the undesired optical carrier signal. A comprehensive mathematical analysis has been accomplished to evaluate the system's performance, and the obtained results are also validated through simulation findings. The derived results demonstrate that the proposed system is capable of operating over a broad modulation index range extending from 1.5 to 4.5, thereby relaxing the stringent requirements for a constant modulation index. The proposed system generates high‐purity mm‐wave signals with an OSSR of 62.06 dB and an RFSSR of 54.79 dB at a modulation index of 2.6. Moreover, it is also validated that even if the system parameters like modulation index, polarizer rotation angle, and phase difference among RF driving signals deviate from their ideal values to a certain degree, the system performance remains acceptable. The involvement of polarization technique, omission of wavelength‐dependent devices, and a large modulation index operating range make this methodology readily appealing for implementation in radio‐over‐fiber transmissions. [ABSTRACT FROM AUTHOR]

A combination of experimental measurement preparations using pressure and temperature sensors in conjunction with the theory of one-dimensional isentropic flow and mathematical physics analyses is presented as a tool for analysis in this paper. Furthermore, the subsequent development of a nozzle for use in environmental electron microscopy between the specimen chamber and the differentially pumped chamber is described. Based on experimental measurements, an analysis of the impact of the nozzle shaping located behind the aperture on the character of the supersonic flow and the resulting dispersion of the electron beam passing through the differential pumped chamber is carried out on the determined pressure ratio using a combination of theory and mathematical physics analyses. The results show that nozzle shapes causing under-expanded gas outflow from the aperture to the nozzle have a worse impact on the dispersion of the primary electron beam. This is due to the flow velocity control. The controlled reduction in the static pressure curve on the primary electron beam path thus causes a significantly higher course of electron dispersion values than variants with shapes causing over-expanded gas outflow. [ABSTRACT FROM AUTHOR]

In this paper, a new microstrip triplexer is designed to work at 2.5 GHz, 4.4 GHz and 6 GHz for mid-band 5G applications. All channels are flat with three low group delays (GDs) of 0.84 ns, 0.75 ns and 0.49 ns, respectively. Compared to the previously reported works, the proposed triplexer has the minimum group delay. The designed triplexer has 18.2%, 13.7%, 23.6% fractional bandwidths (FBW%) at 2.5 GHz, 4.4 GHz and 6 GHz, respectively. The obtained insertion losses (ILs) are low at all channels. These features are obtained without a noticeable increase in the overall size. A novel and simple resonator is used to design the proposed triplexer, which includes two pairs of coupled lines combined with a shunt stub. A perfect mathematical analysis is performed to find the resonator behavior and the layout optimization. The type of shunt stub is determined mathematically. Also, the smallness or largeness of some important physical dimensions is determined using the proposed mathematical analysis. Finally, the designed triplexer is fabricated and measured, where the measurement results verify the simulations. [ABSTRACT FROM AUTHOR]

In this paper, we consider a diffusive predator-prey system with fear response delay, where a benefit from the ani-predation response in addition to the cost is taken into account. As a step toward understanding the underlying mechanism of the spatiotemporal pattern formations by rigorous mathematical analysis, we are interested in how the joint effects of time delay, the fear effect strength, the carrying capacity, as well as the diffusion rates could affect the complex spatiotemporal pattern formations of the system. In particular, Turing instability of the Hopf bifurcating periodic solutions is investigated in details. To that end, a general formula is derived to determine Turing instability of the Hopf bifurcating periodic solutions for general 2-component delayed-diffusive system. This extends our earlier general results for non-delayed diffusive system to its delayed-diffusive counterparts. Our general formula tends to be new and can be applied to a variety of 2-component delayed-diffusive systems. [ABSTRACT FROM AUTHOR]

Holden described, without mathematical analysis, a kinematical method for constructing from platonic solids polylinks with flat or solid polygonal links. No statement was made about the number of polylinks. Geometric parameters of examples shown were found by trial and error. In the present paper, it is shown that each platonic solid defines a one-parametric manifold of polylinks. The geometry of flat links and of links with circular cross section is expressed in terms of the free parameter. The solution is based on a theorem which generalizes known solutions of special cases. [ABSTRACT FROM AUTHOR]

The Internet of Things (IoT) is the underlying technology that has enabled connecting daily apparatus to the Internet and enjoying the facilities of smart services. IoT marketing is experiencing an impressive 16.7% growth rate and is a nearly USD 300.3 billion market. These eye-catching figures have made it an attractive playground for cybercriminals. IoT devices are built using resource-constrained architecture to offer compact sizes and competitive prices. As a result, integrating sophisticated cybersecurity features is beyond the scope of the computational capabilities of IoT. All of these have contributed to a surge in IoT intrusion. This paper presents an LSTM-based Intrusion Detection System (IDS) with a Dynamic Access Control (DAC) algorithm that not only detects but also defends against intrusion. This novel approach has achieved an impressive 97.16% validation accuracy. Unlike most of the IDSs, the model of the proposed IDS has been selected and optimized through mathematical analysis. Additionally, it boasts the ability to identify a wider range of threats (14 to be exact) compared to other IDS solutions, translating to enhanced security. Furthermore, it has been fine-tuned to strike a balance between accurately flagging threats and minimizing false alarms. Its impressive performance metrics (precision, recall, and F1 score all hovering around 97%) showcase the potential of this innovative IDS to elevate IoT security. The proposed IDS boasts an impressive detection rate, exceeding 98%. This high accuracy instills confidence in its reliability. Furthermore, its lightning-fast response time, averaging under 1.2 s, positions it among the fastest intrusion detection systems available. [ABSTRACT FROM AUTHOR]

In this paper, we consider the inverse scattering problem of identifying a two-layered cavity by internal acoustic measurements under the condition that the interior interface has a mixed transmission boundary condition. We focus on the mathematical analysis of recovering the shape of the interior interface by using the linear sampling method, including reconstructing the surface conductivity by the same measurements. [ABSTRACT FROM AUTHOR]

The analysis of the mathematical and mechanical properties of thermoelastic coupling tensors in anisotropic laminates is the topic of this paper. Some theoretical results concerning the compliance tensors are shown and their mechanical consequences analyzed. Moreover, the case of thermally stable laminates, important for practical applications, is also considered. The study is carried out in the framework of the polar method, a mathematical formalism particularly well-suited for the analysis of planar anisotropic problems, introduced by Prof. G. Verchery in 1979. [ABSTRACT FROM AUTHOR]

We would like to present the ideas of Makoto Matsumoto and András Rapcsák in the projective theory of Finsler spaces. Finally, we give some remarks using of Matsumoto–Rapcsák Theorem. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to analyzing the robust stability of interconnected embedded systems. The paper starts by discussing the challenges associated with designing stable and robust embedded systems, particularly in the context of interconnected systems. The proposed approach combines the H∞ control theory with a new model for interconnected embedded systems, which takes into account the effects of communication delays and data losses. The paper provides a detailed mathematical analysis of the new model and presents several theorems and proofs related to its stability. The effectiveness of the proposed approach is demonstrated through several practical examples, including a networked control system and a distributed sensor network. The paper also discusses the limitations of the proposed approach and suggests several directions for future research. The proposed filter design method establishes a sufficient condition for the asymptotic stability of the error system and the satisfaction of a predefined H∞ performance index for time-invariant bounded uncertain parameters. This is achieved through the use of the strict linear matrix inequalities (LMI) approach and projection lemma. The design is formulated in terms of linear matrix inequalities (LMI). Numerical examples are provided to demonstrate the effectiveness of the proposed filter design methods. [ABSTRACT FROM AUTHOR]

The present paper deals with the kinetic-theoretic description of the evolution of systems consisting of many particles interacting not only with each other but also with the external world, so that the equation governing their evolution contains an additional term representing such interaction, called the 'forcing term'. Firstly, the interactions between pairs of particles are both conservative and nonconservative; the latter represents, among others, birth/death rates. The 'forcing term' does not express a 'classical' force exerted by the external world on the particles, but a more general influence on the effects of mutual interactions of particles, for instance, climate changes, that increase or decrease the different agricultural productions at different times, thus altering the economic relationships between different subsystems, that in turn can be also perturbed by stock market fluctuations, sudden wars, periodic epidemics, and so on. Thus, the interest towards these problems moves the mathematical analysis of the effects of different kinds of forcing terms on solutions to equations governing the collective (that is statistical) behaviour of such nonconservative many-particle systems. In the present paper, we offer a study of the basic mathematical properties of such solutions, along with some numerical simulations to show the effects of forcing terms for a classical prey–predator model in ecology. [ABSTRACT FROM AUTHOR]

This paper investigates a cellular network assisted by unmanned aerial vehicles (UAVs) in the presence of a fluctuating 3-dimensional (3D) antenna beamwidth. The primary objective is to perform an analysis of typical user equipment (T-UE) performance with a specific focus on coverage probability and spectral efficiency (SE) in the presence of fluctuations of 3D antenna beamwidth. Within this analytical framework, the macro base stations (MBSs) are meticulously characterized through the application of an independent 2D homogeneous Poisson point process (PPP), while the low-altitude platforms (LAPs) are described using an independent 3D PPP. The study entails the derivation of association probabilities, determining the likelihood of the T-UE associating with MBSs, line-of-sight LAPs, and non-line-of-sight LAPs. Through rigorous mathematical analysis, the paper formulates precise analytical expressions that encapsulate the association and coverage probabilities, taking into account the inherent variability in the UAV antenna beamwidth. This research focuses on a thorough performance evaluation of the T-UE across diverse network configurations, encompassing LAP density, the transmission power of LAPs, and the critical signal-to-interference ratio threshold. The outcomes of this study distinctly underscore the substantial disruptive impact resulting from fluctuating beamwidth on the performance of the T-UE within the UAV-assisted cellular network. Additionally, this performance is further impacted by larger densities and transmission power of the LAP. Hence, it is imperative to take into account the influence of these fluctuations on network association, coverage, and SE whenever contemplating a UAV-assisted cellular network. [ABSTRACT FROM AUTHOR]

The problems of operating range and costs are the two most critical bottlenecks restricting the extensive application of electric vehicles (EVs) in China and some other countries. There are also some prominent problems in China's EVs, which lead to poor competitiveness of EVs compared with traditional internal combustion engine vehicles. This paper analyzes the key mathematical factors restricting the development and popularization of EVs in China from the aspects of strategic policy, sales situation, and self-problems. For the best-selling family cars in China, select the representative models with the same body structure, and make statistics on various parameters most concerned by consumers, establish a database through data statistics and analysis software. Through summarizing France's standardization development strategy and relevant issues reflected by the development data of its EVs, this paper puts forward the hypothesis leading the development of EVs through standardization to enhance their competitiveness, gives the specific suggestions, and briefly analyzes the feasibility from the aspects of product situation. The research content of this paper provides a certain basis and ideas for the future research work. [ABSTRACT FROM AUTHOR]

Fuzzy logic is becoming one of the most-influential fields of modern mathematics with applications that impact not only other sciences, but society in general. This newly found interest in fuzzy logic is in part due to the crucial role it plays in the development of artificial intelligence. As a result, new tools and practices for the development of the above-mentioned field are in high demand. This is one of the issues this paper was composed to address. To be more specific, a sizable part of fuzzy logic is the study of fuzzy connectives. However, the current method used to generalize them is restricted to the use of basic automorphisms, which hinders the creation of new fuzzy connectives. For this reason, in this paper, a new method of generalization is conceived of that aims to generalize the fuzzy connectives using polynomial automorphism functions instead. The creation of these automorphisms is achieved through numerical analysis, an endeavor that is supported with programming applications that, using mathematical modeling, validate and visualize the research. Furthermore, the automorphisms satisfy all the necessary criteria that have been established for use in the generalization process and, consequently, are used to successfully generalize fuzzy connectives. The result of the new generalization method is the creation of new usable and flexible fuzzy connectives, which is very promising for the future development of the field. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to examine the impact of moisture and temperature changes on the behavior of a semi-infinite solid cylinder made of T300/5208 composite material. This study aims to provide analytical solutions for temperature, moisture and thermal stress through the de-coupling technique and the method of integral transforms. Both coupled and uncoupled cases are considered. Design/methodology/approach: This study investigates the hygrothermo-elastic response of a semi-infinite solid circular cylinder using an integral transform technique that includes Hankel and Fourier transforms. The cylinder is subjected to prescribed sources, and a numerical algorithm is developed for the numerical computation of the results. The goal is to understand how the cylinder responds to changes in temperature and moisture. Findings: The paper presents an analytical solution for temperature, moisture and thermal stress in a semi-infinite solid cylinder obtained through the use of an integral transform technique. The study focuses on a graphite fiber-reinforced epoxy matrix composite material (T300/5208) and discusses the coupled and uncoupled effects of temperature, moisture and thermal stress on the material. The results of the transient response hygrothermo-elastic field are presented graphically to provide a visual representation of the findings. Research limitations/implications: The research presented in this article is primarily hypothetical and focused on the analysis of mathematical models. Originality/value: To the authors' best knowledge, this study is the first to investigate the hygrothermal effect in a semi-infinite circular cylinder. Additionally, the material properties used in the analysis are both homogenous and isotropic and independent of both temperature and moisture. These unique aspects of the study make it a novel contribution to the field. [ABSTRACT FROM AUTHOR]

In the paper "The non‐Riemannian nature of perceptual color space," the authors analyze the data of visual experiments conducted using triad of CIE L* achromatic stimuli. The statistical analysis of their results leads them to claim that the L* axis cannot be endowed with a Riemannian metric coherent with observers' responses. In this communication we provide a mathematical analysis which, in our opinion, refutes the main claim of the quoted paper. Furthermore, we raise questions on the soundness of using an achromatic perceptual coordinate to describe non‐chromatic perception. We inform about an alternative in which achromaticity emerges from the very act of observing colors (Provenzi E. SIAM J Imag Sci, 15(4):1944–1976, 2022; Berthier M, Provenzi E. Proc R Soc A, 478(2258):20210508, 2022). [ABSTRACT FROM AUTHOR]

This paper is devoted to the analysis of mathematical models of chemotherapy for malignant tumors growing according to the Gompertz law or the generalized logistic law. The influence of the therapeutic agent on the tumor dynamics is determined by a therapy function depending on the time-varying concentration of the drug in the patient's body. The case of a non-monotonic therapy function with two maxima is studied. It reflects the use of two different therapeutic agents. The state variables of the dynamics are the tumor volume and the amount of the therapeutic agent able to suppress malignant cells (concentration of the drug in the body). The treatment protocol (the rate of administration of the therapeutic agent) is the control in the dynamics. The optimal control problem for this models is considered. It is the problem of the construction of treatment protocols that provide the minimal tumor volume at the end of the treatment. The solution of this problem was obtained by the authors in previous works via the optimal control theory. The form of the considered therapy functions provides a specific structure for the optimal controls. The managerial insights of this structure are discussed. In this paper, the structure of the viability set is described for the model according to the generalized logistic law. It is the set of the initial states of the model for which one can find a treatment protocol that guarantees that the tumor volume remains within the prescribed limits throughout the treatment. The description of the viability set's structure is based on the optimal control theory and the theory of Hamilton–Jacobi equations. An inverse problem of therapy is also considered, namely the problem of reconstruction of the treatment protocol and identification of the unknown parameter of the intensity of the tumor growth. Reconstruction is carried out by processing information about the observations of the tumor volume dynamics and the measurements of the drug concentration in the body. A solution to this problem is obtained through the use of a method based on the calculus of variations. The results of the numerical simulations are presented herein. [ABSTRACT FROM AUTHOR]

The Ebola virus continues to be the world's biggest cause of mortality, especially in developing countries, despite the availability of safe and effective immunization. In this paper, we construct a fractional-order Ebola virus model to check the dynamical transmission of the disease as it is impacted by immunization, learning, prompt identification, sanitation regulations, isolation, and mobility limitations with a constant proportional Caputo (CPC) operator. The existence and uniqueness of the proposed model's solutions are discussed using the results of fixed-point theory. The stability results for the fractional model are presented using Ulam–Hyers stability principles. This paper assesses the hybrid fractional operator by applying methods to invert proportional Caputo operators, calculate CPC eigenfunctions, and simulate fractional differential equations computationally. The Laplace–Adomian decomposition method is used to simulate a set of fractional differential equations. A sustainable and unique approach is applied to build numerical and analytic solutions to the model that closely satisfy the theoretical approach to the problem. The tools in this model appear to be fairly powerful, capable of generating the theoretical conditions predicted by the Ebola virus model. The analysis-based research given here will aid future analysis and the development of a control strategy to counteract the impact of the Ebola virus in a community. [ABSTRACT FROM AUTHOR]

A generalization of the problem of writing on dirty paper is considered in which one transmitter sends a common message to multiple receivers. Each receiver experiences on its link an additive interference (in addition to the additive noise), which is known noncausally to the transmitter but not to any of the receivers. Applications range from wireless multiple-antenna multicasting to robust dirty paper coding. We develop results for memoryless channels in Gaussian and binary special cases. In most cases, we observe that the availability of side information at the transmitter increases capacity relative to systems without such side information, and that the lack of side information at the receivers decreases capacity relative to systems with such side information. For the noiseless binary case, we establish the capacity when there are two receivers. When there are many receivers, we show that the transmitter side information provides a vanishingly small benefit. When the interference is large and independent across the users, we show that time sharing is optimal. For the Gaussian case, we present a coding scheme and establish its optimality in the high signal-to-interference-plus-noise limit when there are two receivers. When the interference power is large and independent across all the receivers, we show that time-sharing is again optimal. Connections to the problem of robust dirty paper coding are also discussed. [ABSTRACT FROM AUTHOR]

Abstract: The study used the simulated e-paper to investigate how the bending radius of curvature (−10cm, plane, and 10cm) and 12 text/background color-combinations of e-paper affect subjects’ visual performance and subjective preference under various ambient illuminance conditions (200 and 500lx). Analysis results indicated that the bending curvature and ambient illuminance did not significantly affect subjects’ visual performance. However, subjects visual performance differed significantly for different text/background color combinations of the simulated e-paper. When the background color of the simulated e-paper was set to yellow-like condition and the luminance of the text was low (2.2 and 4.6cd/m2), subjects’ visual performance was best. Regarding the subjective preferences of subjects, the results of this research also demonstrated that the bending curvature, text/background color combinations and ambient illuminance all significantly affected the subjective preferences of subjects. Subjects exhibited the best preference under the following settings: bending curvature of the simulated e-paper set to plane; background color of the simulated e-paper set to yellow-like condition and low text luminance (2.2 or 4.6cd/m2); high ambient illuminance (500lx). [Copyright &y& Elsevier]

We show that the result on cyclic weak contractions of Harjani et al. (J. Nonlinear Sci. Appl. 6:279-284, ) holds without the assumption of compactness of the underlying space, and also without the assumption of continuity of the given mapping. [ABSTRACT FROM AUTHOR]

With this note, we want to open a discussion on the duality theory for Interval Optimization. We begin by showing that some duality results Wu ( J Optim Theory Appl 144:615-628, ) are useless. [ABSTRACT FROM AUTHOR]

The purpose of the present note is to point out mathematical mistakes in some published papers on boundary value problems to prevent usage of mistaken results and methods by mathematicians. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This special issue of the Journal Mathematical Methods in the Applied Sciences on the topic of Modelling, Analysis, and Applications is devoted to the development of mathematical modelling, analysis, and applications, from theoretical and numerical perspectives, involving different applied sciences and engineering. It collects invited contributions, from selected quality full papers submitted to the International Conference on Mathematical Analysis and Applications in Science and Engineering (ICMA2SC2022). The conference took place in Porto, Portugal in 27–29 June 2022 (https://www.isep.ipp.pt/Page/ViewPage/ICMASC). [ABSTRACT FROM AUTHOR]