In this paper, we introduce the notions of upper and lower c-\tau^\star(\sigma_1,\sigma_2)-continuous multifunctions. Moreover, we investigate several characterizations and some properties concerning upper and lower c-\tau^\star(\sigma_1,\sigma_2)-continuous multifunctions.
In this paper, we introduce the notions of upper almost nearly \tau^\star(\sigma_1,\sigma_2)-continuous multifunctions and lower almost nearly \tau^\star(\sigma_1,\sigma_2)-continuous multifunctions. Moreover, we investigate several characterizations of upper almost nearly \tau^\star(\sigma_1,\sigma_2)-continuous multifunctions and lower almost nearly \tau^\star(\sigma_1,\sigma_2)-continuous multifunctions.
In this work, we develop a Korteweg-de Vries model for weakly nonlinear long waves propagating over uneven bathymetry in the presence of surface tension and a spatially and temporally varying tidal current. The tidal contribution is introduced through both local advection and a current-dependent dispersive correction so that its effect cannot, in general, be absorbed into a static modification of the bottom. The model retains a quadratic conservation structure and is placed within a standard variable-coefficient well-posedness framework. A midpoint finite-difference approximation is constructed to preserve the corresponding discrete invariant. Numerical experiments over a normalized tidal cycle investigate several current amplitudes, compare transport-only and current-dispersive effects, and demonstrate the distinct influence of tidal forcing on wave propagation. The results provide a reduced-order framework for studying wave--current interaction in shallow coastal environments where bathymetry, capillarity, and tidal motion act simultaneously.
In this paper, we introduce and formally define another variant of hop domination in a graph called accurate hop domination. We investigate this new concept on some families of graphs and graphs under some binary operations. In addition, we characterize accurate hop dominating sets and we use these results to derive some formulas of accurate hop domination numbers for the said graphs. Moreover, we establish some connections of this newly defined concept with other well-known concepts in graph theory such as hop domination theory.
We present a one-parameter generalization of rectangle flanks of a triangle. Given an arbitrary triangle and a positive real number k, first-order rectangle flanks are constructed externally on the three sides so that each flank side is k times the corresponding free side. The outer free sides determine three associated triangle flanks, on which second-order rectangle flanks are constructed with the same parameter. We prove that the ratio of the total area of the second-order rectangle flanks to the total area of the first-order rectangle flanks is 3/k^2, independently of the shape of the initial triangle. This result unifies the two previously known cases k=1 and k=2.
Necessary conditions under which the non-deterministic operation on the set of formula languages can be applied to the set of formula languages of a fixed variable are determined.
The vertex cover problem is a fundamental concept in graph theory and computational complexity, widely studied due to its practical applications in network and optimization. In this paper, we present a new variation of the vertex cover problem known as the co-certified vertex cover. We explore this concept across different families of graphs and analyze its behavior under some graph operations. We examine how the co-certified vertex cover relates to the standard vertex cover concept. Through this analysis, we provided a clearer understanding of this new concept and its potential applications in graph theory and computational problems.
In this paper, we present several characterizations of upper almost m(\sigma_1,\sigma_2)-continuous multifunctions and lower almost m(\sigma_1,\sigma_2)-continuous multifunctions via (\sigma_1,\sigma_2)p-open sets.
In this paper, we introduce a new variant of zero forcing, called K-hop zero forcing. We study this concept and its behavior in some classes of graphs such as complete and the join of a trivial graph and a path graph with order n. Moreover, we investigate its K-propagation time, the minimum number of steps for a minimum K-hop zero forcing set to K-force all other uncolored vertices in the said graphs. Furthermore, we derive simplified formulas for the K-hop zero forcing number and K-propagation time of the said graphs.
In this paper, we investigate some characterizations of upper almost m(\sigma_1,\sigma_2)-continuous multifunctions and lower almost m(\sigma_1,\sigma_2)-continuous multifunctions.
We prove few structural properties of group nearring modules involving essential ideal of nearring module and those of group nearring module.
Let G be a graph with vertex-set and edge-set V(G) and E(G), respectively. Then S \subseteq V(G) is a hop independent J-dominating if S is both a hop independent and J-dominating set of G. The maximum cardinality of a hop independent J-dominating set of G, denoted by \gamma^{hi}_{J}(G) is the hop independent J-domination number of G. In this paper, we initiate the study on hop independent J-domination of a graph. We characterize the hop independent J-dominating sets in some special graphs, join of two graphs, and we derive some bounds or formulas of the said parameter of each of these graphs.
In this paper, we give an algebraic framework for goodness-of-fit testing in discrete data models. A statistical model is encoded by an integer matrix A, its conditional reference set is the fiber F_{Au}, and feasible sampling inside the fiber is governed by a Markov basis of the toric ideal I_A. We establish the Markov-basis connectivity theorem, the finite-sample validity of exact conditional testing, and the irreducibility of Markov-chain sampling on a fiber. This framework emphasizes sparse contingency tables, log-linear models and network models, where asymptotic chi-square approximations may be unreliable.
In this paper, we generalize some inequalities for the modulus of the derivative of rational functions. We establish a new bound for the modulus of the derivative of rational functions with flexible number of zeros. Existing results are recovered as special cases of our theorems.
In this paper, algebras of tree languages induced by full terms that preserve a partition on a finite set are introduced. The fact that the binary operation +_n on the Cartesian product of the set of full terms that preserve a partition and the set of tree languages induced by full terms that preserve a partition is associative is proved. Furthermore, the algebra of quantifier free formula of tree languages defined by full terms that preserve a partition is constructed.
The number of arrivals is a discrete variable and hence is a count data. In the present study, we focus on analyzing the arrival of students to the lending section of a library. Various count regression models are applied to analyze the data statistically. With a limited covariate terms, we observe that a zero-inflated negative binomial regression model best fits the available data.
In this study, we investigate whether the sum of nonnegative powers of the consecutive integers 52 and 53 can be expressed as a perfect square. In particular, we examine the Diophantine equation 53^x+52^y=z^2 within the framework of elementary number theory and show that the equation admits no integer solutions.
In this paper, we present a deep learning framework designed to predict carbon footprint (CF) by integrating power quality metrics. We evaluate five deep learning architectures (LSTM, GRU, BiLSTM, CNN-LSTM, and Stacked LSTM) against statistical benchmarks. The GRU model demonstrate the highest predictive accuracy. Beyond prediction, we explore the causal drivers of emissions. Granger causality tests identified total harmonic distortion (THDi) as a significant predictor of CF (F = 11.27, p < 0.001). Moreover, the SEM reveals a direct causal link between THDi exceedance and emission spikes (\beta = 0.413, p < 0.001), where each percentage-point increase in harmonic violation correlates to a 4.2-7.8 % rise in CF. These findings suggest that real-time harmonic monitoring, paired with GRU-based forecasting, provides a practical framework for supporting industrial net-zero transitions.
A compact fixed-accuracy sequential procedure is developed for finite-dimensional parameters of Markov-dependent observations. Sampling is stopped when the largest semi-axis of the likelihood confidence ellipsoid, computed from the observed information matrix, is not larger than a prescribed tolerance. Under identifiability, ergodicity, smooth likelihood derivatives, nonsingular Fisher information, and random-index stability, the stopped maximum likelihood estimator is strongly consistent and asymptotically normal. The final ellipsoid has asymptotic coverage probability 1-\alpha, and the stopping time is first-order efficient relative to the ideal fixed sample size that would be chosen if the true Fisher information were known.
In this work, we generalize the Dreidel game using an m-sided top and analyzes the expected payoff for each player under fair and biased conditions. We derive a general formula for the expected payoff on the n^{th} roll and determine the conditions for fairness. Specifically, the game is equitable if and only if the total penalty across all sides equals half the initial value of the central pot. If the total penalty exceeds this threshold, the first player is disadvantaged; otherwise, the first player gains a statistical advantage.
