Search Results (3,940)

There are two aims in this paper. One is to completely characterize complex symmetric and 2-complex symmetric weighted composition operators induced by some special symbols on the weighted Bergman space of the unit ball, and the other is to fully characterize the complex symmetry of the difference of such operators on the space. Full article

For each n-dimensional real Banach space X and each positive integer m, let $\beta (X,m)$ be the infimum of $\delta \in (0,1]$ such that each set $A\subseteq X$ having diameter 1 can be represented as the union of m subsets of A, whose diameters are not greater than $\delta$. Providing accurate estimations of $\beta (X,m)$ for specific choices of X and m is crucial for addressing the extension of the classical Borsuk’s problem. A general framework for estimating $\beta (X,m)$ via constructing and refining universal covering systems is presented. As an example, a universal covering system is constructed in ${\ell }_1^3$ and it is shown that $\beta ({\ell }_1^3,8)\le 11/12$ by a feasible partitioning of members in this universal covering system. Full article

In this article, we introduce a distribution that is an extension of the Power Maxwell (PM) distribution, which is based on the quotient of two independent random variables. These are the PM and a gamma distribution, respectively. In this way, the result is a model with greater kurtosis than the PM distribution. We study its probability density function and some properties, such as moments, asymmetry and kurtosis coefficient. An EM algorithm is proposed to estimate the parameters via the maximum likelihood method. A simulation study is carried out to study the asymptotic behaviour of our estimators. An application to a real dataset is also included. Full article

With the advancement of science and technology, industrial robots have become indispensable equipment in advanced manufacturing and a critical benchmark for assessing a nation’s manufacturing and technological capabilities. Enhancing the reliability of industrial robots is therefore a pressing priority. This paper investigates the drive system of industrial robots, modeling it as a series system comprising multiple components (n) with a repairman who operates under a single vacation policy. The system assumes that each component’s lifespan follows an exponential distribution, while the repairman’s repair and vacation times adhere to general distributions. Notably, the repairman initiates a vacation at the system’s outset. Using the supplementary variable method, a mathematical model of the system is constructed and formulated within an appropriate Banach space, leading to the derivation of the system’s abstract development equation. Leveraging functional analysis and the $C_0$-semigroup theory of bounded operators, the study examines the system’s adaptability, stability, and key reliability indices. Furthermore, numerical simulations are employed to analyze how system reliability indices vary with parameter values. This work contributes to the field of industrial robot reliability analysis by introducing a novel methodological framework that integrates vacation policies and general distribution assumptions, offering new insights into system behavior and reliability optimization. The findings have significant implications for improving the design and maintenance strategies of industrial robots in real-world applications. Full article

This paper presents a multiparty quantum private comparison (MQPC) protocol that facilitates multiple users to compare the equality of their private inputs while preserving the confidentiality of each input through the principles of quantum mechanics. In our approach, users initially convert their secret integers into binary representations, which are then encoded into single photons that act as carriers of the information. These encoded single-photon states undergo encryption via rotational operations, effectively obscuring the original inputs before transmission to a semi-honest third party (TP). The TP decrypts the quantum states and conducts Z-basis measurements to derive the comparison results. To enhance security, the protocol incorporates decoy photons, enabling participants to detect potential eavesdropping on the quantum channel. Importantly, even if the TP or other participants attempt to glean insights into each other’s inputs, the encryption via rotational operations ensures that private information remains inaccessible. This protocol demonstrates significant advancements in practicality compared to existing MQPC frameworks that rely on complex quantum technologies, such as entanglement swapping and multi-particle entanglement. By leveraging the simplicity of single photons, rotation operations, and Z-basis measurements, our protocol is more accessible for implementation. Full article

Benford’s Law describes the effect of specific first significant digit probability distribution in natural datasets. In the case of non-natural or artificial intervention within such datasets, the first digit probability distribution tends to deviate from the theoretical distribution. Thus, Benford’s Law-based methods are useful in detecting unnatural changes in datasets indicating artificial manipulation of the original data. In our article, we first briefly describe the theory behind this law with an overview of Benford’s Law’s properties. We then focus on conformity tests for Benford’s Law as methods for data change detection compared with the original dataset. In our research, the datasets were collected from electricity consumption metering devices. We provide the results of conformity with Benford’s Law for affected datasets within a series of simulations with different affecting operations. We found a research gap when comparing the deviation from a theoretical first-digit probability distribution for different operations affecting the original dataset. We have made a series of simulations with different affecting operations and we tried to determine the effectiveness thresholds for each operation. As shown in the results section, different intervention operations manifest different specific thresholds of such deviations from Benford’s Law’s distribution. Full article

Generically, in a system with more than three point vortices, there exist regions of stability around each vortex, even if the system is chaotic. These regions are usually called stability islands, and they have a morphology that is hard to characterize. In a system of two or three point vortices, these stability islands are better named vortex atmospheres or atmospheric islands, since the whole system is regular. In this work, we present an analytical study to characterize these atmospheres in two point vortex systems for arbitrary values of the circulations ${\mathrm{\Gamma }}_1$ and ${\mathrm{\Gamma }}_2$ in the infinite two-dimensional plane $\left(x,y\right)\in {\mathbb{R}}^2$—the simplest scenario—by studying the dynamics of passive particles in these environments. We use the trajectories of passive particles to find the stagnation points of these systems, the special trajectories that partition ${\mathbb{R}}^2$ in different regions and the analytical expressions that define the boundary of the atmospheric islands. In order to characterize the geometry of these atmospheres, we compute their perimeter and area as a function of $\gamma ={\displaystyle \frac{{\mathrm{\Gamma }}_1}{{\mathrm{\Gamma }}_1+{\mathrm{\Gamma }}_2}},$ if ${\mathrm{\Gamma }}_1+{\mathrm{\Gamma }}_2\ne 0.$ The case ${\mathrm{\Gamma }}_1+{\mathrm{\Gamma }}_2=0$ is treated separately, as the perimeter and area of the atmospheres do not depend on the circulations. Furthermore, in this latter case, we observe that the atmospheric island has a very similar morphology to an ellipse, only differing from the ellipse that best approximates the atmosphere by a relative error of $\approx$3.76‰ in area. Full article

The concept of strong atoms in Q-algebras is discussed herein. In this work, some properties of strong atoms are provided. We show that there is no Q-algebra X with $\left|X\right|\ge 3$ such that all elements are strong atoms. We also find that any two-element subset of X containing a constant 0 is a subalgebra of X whenever X contains a strong atom. Moreover, any subset of X with the cardinality equal to 3 containing a strong atom and a constant 0 is always a subalgebra. We present some results concerning the concept of an ideal. In a Q-algebra X that contains a strong atom, any ideal of X is a subalgebra of X. An ideal of a Q-algebra X that is induced by any subset containing a strong atom is equal to X. Furthermore, we show that, for any Q-algebra X with a strong atom, there is only one ideal containing a strong atom. In particular, for $\left|X\right|\le 4$, we propose that a finite union of ideals of X is again an ideal of X. Full article

In this work, by using one dynamic Gronwall–Bihari-type integral inequality on time scales, an interesting asymptotic behavior property of high-order nonlinear dynamic equations on time scales was obtained, which also generalized two classical results belong to Máté and Nevai’s and Agarwal and Bohner’s, respectively. Full article

Neutral transmission line models are essential for analyzing stability and periodicity in systems influenced by nonlinear and delayed dynamics, particularly in modern smart grids. This study utilizes Krasnoselskii’s fixed-point theorem to establish sufficient conditions for the existence and asymptotic stability of periodic solutions, eliminating the need for differentiability in delay terms and coefficients. The results extend existing findings and are validated through a single test example, demonstrating the theoretical applicability of the proposed approach. These findings provide a mathematical framework for understanding the behavior of power distribution systems under nonlinear and delayed influences. Full article

This article establishes the existence of fixed points and common fixed points for set-valued mappings satisfying an implicit-type contraction inequality involving a new auxiliary function in a complete metric space equipped with a binary relation. Through a novel family of functions referred to as the $\Delta$-family, which simplifies the axioms in comparison to the previously defined $\Phi$-family, the study unifies a few classical fixed-point theorems. The practical relevance of the theoretical findings is demonstrated by applying the results to investigate the existence of solutions for a system of integral equations. Full article

It is a famous hypothesis that orbifold D-brane charges in string theory can be classified in twisted equivariant K-theory. Recently, it is believed that the hypothesis has a non-trivial lift to M-branes classified in twisted real equivariant 4-Cohomotopy. Quasi-elliptic cohomology, which is defined as an equivariant cohomology of a cyclification of orbifolds, potentially interpolates the two statements, by approximating equivariant 4-Cohomotopy classified by 4-sphere orbifolds. In this paper we compute Real and complex quasi-elliptic cohomology theories of 4-spheres under the action by some finite subgroups that are the most interesting isotropy groups where the M5-branes may sit. The computation connects the M-brane charges in the presence of discrete symmetries to Real quasi-elliptic cohomology theories, and those with the symmetry omitted to complex quasi-elliptic cohomology theories. Full article

The main aim of this paper is to investigate the existence and uniqueness of solutions for some classes of abstract degenerate non-scalar Volterra equations on the line. In order to achieve our aims, we essentially apply the vector-valued Fourier transform. We use the class of $(A,k,B)$-regularized C-pseudoresolvent families in our analysis as well, and present several useful remarks and illustrative applications of the established results. Full article

The present work investigates the spatial evolution characteristics of solutions to the Moore–Gibson–Thompson heat equation within a three-dimensional cylindrical geometry. By constructing an integral-differential inequality framework, we establish rigorous estimates demonstrating the exponential spatial decay of the solution as the axial distance from the inlet boundary increases without bound. This finding aligns with a generalized interpretation of the Saint-Venant principle, demonstrating its applicability under the present asymptotic conditions. The integral-differential inequality method proposed in this paper can also be used for the study of the Saint-Venant principle for other equations. Full article

This paper introduces a novel 3D periodically forced extended Lorenz-like system and illustrates a single thick two-scroll attractor with potential unboundedness whose time series of the second state variable present some certain random characteristics rather than pure periodicity yielded by that system itself. Combining the Lyapunov function and the definitions of both the $\alpha$-limit set and $\omega$-limit set, the following rigorous results are proved: infinitely many heteroclinic orbits to two families of parallel parabolic-type non-hyperbolic equilibria, two families of infinitely many pairs of isolated equilibria, an infinite set of isolated equilibria, and infinitely many pairs of isolated equilibria. Full article