Seyed M Mousavian, Shah J Miah, James Skinner
et al.
Despite the proliferation of video analytics applications supported by deep learning (DL) methods in various service sectors, the potential of such technologies for hospitality decision support remains at an emergent stage. While issues have been persistent for researchers, this study identifies a real-world business problem in hospitality: the lack of insight into crowds (potential customers) needed to provide customized services and design promotional offers based on family demographics. To bridge this gap, through the lens of design science, this study introduces a DL-based video analytics solution (artifact) to detect and track potential customers, according to their family size, specifically identifying individuals, couples, and groups. Using 25 hours of CCTV footage, a DL model combining YOLOv11 and BYTEtrack was trained and developed (i.e. demonstrated as a software prototype) to detect and track individuals, couples, and groups. Initial evaluation results show strong performance, indicating that the model is suitable for further refinement and potential commercial application. This paper addresses a practical gap in hospitality operations by showing how a DL-based video analytics can generate insightful visual cues to support informed managerial decision-making.
Niloofar Heidarikohol, Mehmet Engin Tozal, Mehedi Hassan
In this exploratory study, we examine the impact of vaccination on the SARS-CoV-2 spread pattern in various US states. Using time-series data from the Johns Hopkins University, we apply Dynamic Time Warping (DTW)–based hierarchical clustering to identify groups of states exhibiting similar SARS-CoV-2 spread patterns. We introduce a three-stage segmentation framework, using Matrix Profile, that divides a 450-day observation period into three analytically distinct stages: Early, Middle, and Post stages. The study is motivated by the goal of facilitating a proper representation to study the impact of vaccination, and minimizing the ramifications of future outbreaks by devising effective vaccination strategies. Our findings suggest that many states showed decreases in confirmed cases during the early period following vaccination rollout. This pattern did not persist uniformly across the later Post stage, during which fluctuations in confirmed cases coincided with factors such as changes in social behaviour and the emergence of new variants. The observed associations illustrate shifts in spread patterns across states over time. Our study is limited by its focus on US states and by the use of public vaccination timelines rather than individual-level vaccination or confirmed cases data.
The article focuses on the initial problem for a third-order linear integro-differential equation with a small parameter at the higher derivatives, assuming that the roots of the additional characteristic equation have opposite signs. This paper presents a fundamental set of solutions and initial functions for a singularly perturbed homogeneous differential equation. The solution to the singularly perturbed initial integrodifferential problem employs analytical formulas. A theorem concerning asymptotic estimates of the solution is established.
The transmission mechanisms of most infectious diseases are generally well understood from an epidemiological standpoint. To mathematically and quantitatively characterize the spread of these diseases, various classical epidemic models-such as the SIR, SIS, SEIR, and SIRS frameworks-have been formulated and thoroughly investigated. In the present paper, the initial value problem for the system of semilinear parabolic differential equations arising in epidemic models with a general semilinear incidence rate in a Hilbert space with a self-adjoint positive definite operator is investigated. The main theorem on the existence and uniqueness of bounded solutions for this system is established. In applications, theorems on the existence and uniqueness of bounded solutions for two types of systems of semilinear partial differential equations arising in epidemic models are proved. A first-order accurate finite difference scheme is developed to construct approximate solutions for this system. We further prove a theorem that guarantees the existence and uniqueness of bounded solutions for the discrete problem, independently of the time step. The theoretical results are supported by applications, where bounded solutions of the continuous system and their corresponding discrete approximations are demonstrated. Finally, numerical results are presented to illustrate the effectiveness and accuracy of the proposed scheme.
In this article, the existence and uniqueness of solutions for non-linear fractional differential equation with Tempered Ψ−Caputo derivative with three-point boundary conditions were studied. The existence and uniqueness of the solution were proved by applying the Banach contraction mapping principle and Schaefer’s fixed point theorem.
In this paper, the boundary value problem of heat conduction in a domain was considered, boundary of which changes with time, as well as there is no the problem solution domain at the initial time, that is, it degenerates into a point. To solve the problem, the method of heat potentials was used, which makes it possible to reduce it to a singular Volterra type integral equations of the second kind. The peculiarity of the obtained integral equation is that it fundamentally differs from the classical Volterra integral equations, since the Picard method is not applicable to it and the corresponding homogeneous integral equation has a nonzero solution.
The paper defines a new class of algebras, the theory of which is a special case of Jonsson theories. This class applies to both varieties and Jonsson theories. The main results of this article are the following two results. In this article, an answer is obtained to the question of the equivalence of existential closure and algebraic closure of the model of the cosemantic class of a fixed spectrum of a Robinson hereditary variety. A criterion for strong minimality is obtained in the framework of the study of central types of central classes and fragments of a fixed spectrum.
Zacharij Niemcevski (1766–1820) was a professor of higher mathematics at the Vilnius university in the period from 1797 until 1820. He was a member correspondent of Societe Academique des sciences and Academie Imperial des Sciences de Turin. Niemcevski tought differential and integral calculus by the tracktate of S.F. Lacroix, analytic geomety – by J.B. Biot, and mechanics – by L.B. Francoeur. His investigations on the Lithuanian language was published in the tractate of K. Malte Brun.
This paper addresses the solution of a differential-difference type equation having an interior layer behaviour. A difference scheme is suggested to solve this equation using a non-standard finite difference method. Finite differences are derived from the first and second order derivatives. Using these approximations, the given equation is discretized. The discretized equation is solved using the algorithm for the tridiagonal system. The method is examined for convergence. Numerical examples are illustrated to validate the method. Maximum errors in the solution, in contrast to the other methods are organized to justify the method. The layer behaviour in the solution of the examples is depicted in graphs.
In this study, we present an investigation of the asymptotic behavior of solutions of sum-difference equations. Based on some mathematical inequalities, we have obtained our results. The obtained results can apply to some fractional type difference equations as well.
Marcel Veismann, Christopher Dougherty, Morteza Gharib
Rotorcraft can encounter highly unsteady flow when descending at a steep angle, leading to a flow condition called vortex ring state, which is associated with strong oscillatory airloads and substantial losses in mean rotor thrust. This study examines the aerodynamic coupling between closely arranged rotors in vertical flight and assesses the extent to which rotor–rotor interactions affect the rotor performance in this flight stage. Wind tunnel experiments were performed on a small-scale, dual-rotor set-up with adjustable rotor spacing, and the effect of rotor separation on thrust generation was quantified. Pairs of 4 in., 5 in. and 6 in. rotors ($3.0 \times 10^4< Re<8.1 \times 10^4$) were investigated, with load cell measurements showing significant thrust losses and concomitantly increased thrust oscillations as descent rate increased. Peak losses and fluctuations were consistently recorded at descent rates of 1.2–1.3 times the hover induced velocity for all rotor sizes and separations. While tests showed that the mean aerodynamic performance of dual-rotor systems is generally similar to that of single rotors, appreciable changes to the descent characteristics could be observed at low rotor separations. Particle image velocimetry flow visualization suggests considerable changes to the flow field as rotor separation decreases, where individual vortex ring systems merge into a single vortex ring structure.
The statistical convergence is defined for sequences with the asymptotic density on the natural numbers, in general. In this paper, we introduce the statistical convergence in vector lattices by using the finite additive measures on directed sets. Moreover, we give some relations between the statistical convergence and the lattice properties such as the order convergence and lattice operators.
A methodology for defining variational principles for a class of PDE models from continuum mechanics is demonstrated, and some of its features explored. The scheme is applied to quasi-static and dynamic models of rate-independent and rate-dependent, single crystal plasticity at finite deformation.
In this paper we study the problem of the best approximation by linear methods of solutions to one Triebel-type equation. This problem was solved by using estimates of the linear widths of the unit ball in corresponding spaces of differentiable functions. According to the definition, linear widths give the best estimates for the approximation of compact sets in a given normed space by linear methods which are implemented through finite-dimensional operators. The problem includes answers to the questions about the solvability of the studied equation, the construction of the corresponding weighted space of differentiable functions, the development of a method for estimating linear widths of compact sets in weighted polynomial Sobolev space. In this work, conditions are obtained under which the considered operator has a bounded inverse. The weighted Sobolev space corresponding to the posed problem is determined. Upper estimates are obtained for the counting function for a sequence of linear widths, which correspond to the posed problem. One example is constructed in which two-sided estimates of linear widths are given. The method for solving this problem can be applied to the numerical solution of non-standard ordinary differential equations on an infinite axis.
Soft topological polygroups are defined in two different ways. First, it is defined as a usual topology. In the usual topology, there are five equivalent definitions for continuity, but not all of them are necessarily established in soft continuity. Second it is defined as a soft topology including concepts such as soft neighborhood, soft continuity, soft compact, soft connected, soft Hausdorff space and their relationship with soft continuous functions in soft topological polygroups.
Gandhimohan M. Viswanathan, Marco Aurelio G. Portillo, Ernesto P. Raposo
et al.
An exact solution of the Ising model on the simple cubic lattice is one of the long-standing open problems in rigorous statistical mechanics. Indeed, it is generally believed that settling it would constitute a methodological breakthrough, fomenting great prospects for further application, similarly to what happened when Lars Onsager solved the two-dimensional model eighty years ago. Hence, there have been many attempts to find analytic expressions for the exact partition function <i>Z</i>, but all such attempts have failed due to unavoidable conceptual or mathematical obstructions. Given the importance of this simple yet paradigmatic model, here we set out clear-cut criteria for any claimed exact expression for <i>Z</i> to be minimally plausible. Specifically, we present six necessary—but not sufficient—conditions that <i>Z</i> must satisfy. These criteria will allow very quick plausibility checks of future claims. As illustrative examples, we discuss previous mistaken “solutions”, unveiling their shortcomings.
We investigate the impact of a presumed axion-like-particle (ALP) emission in a core-collapse supernova explosion on neutrino luminosities and mean energies employing a relatively simple analytic description. We compute the nuclear Bremsstrahlung and Primakoff axion luminosities as functions of the protoneutron star (PNS) parameters and discuss how the ALP luminosities compete with the neutrino emission, modifying the total PNS thermal energy dissipation. Our results are publicly available in the python package ARtiSANS, which can be used to compute the neutrino and axion observables for different choices of parameters.
Fracture mechanics is crucial for many fields of engineering, as precisely predicting failure of structures and parts is required for efficient designs. The simulation of failure processes is, from a mechanical and a numerical point of view, challenging, especially for inhomogeneous materials, where the microstructure influences crack initiation and propagation and leads to complex crack patterns. The phase field method for fracture is a promising approach to encounter such materials since it is able to describe complex fracture phenomena like crack kinking, branching and coalescence. Moreover, it is a largely mesh independent approach, given that the mesh is homogenous around the crack. However, the broadly used formulation of the phase field method is limited to isotropic materials and does not account for preferable fracture planes defined through the material's microstructure. In this work, the method is expanded to take orthotropic constitutive behavior and preferable directions of crack propagation into account. We show that by using a stress-based split and multiple phase field variables with preferable fracture planes, in combination with a hybrid phase field approach, a general framework can be found for simulating anisotropic, inhomogeneous materials. The stress-based split is based on fictitious crack faces and is, herein, expanded to anisotropic materials. Furthermore, a novel hybrid approach is used, where the degradation of the sound material is performed based on a smooth traction free crack boundary condition, which proves to be the main driving factor for recovering observed crack patterns. This is shown by means of a detailed analysis of two examples: a wooden single edge notched plate and a wood board with a single knot and complex fiber directions. In both cases, the proposed novel hybrid phase field approach can realistically reproduce complex failure modes.