East West Math http://eastwestmath.org/index.php/ewm en-US nhbtrung@ntt.edu.vn (Trung, Nguyen Hoang Bao) Mon, 28 Jul 2025 14:56:39 +0800 OJS 3.1.2.1 http://blogs.law.harvard.edu/tech/rss 60 EXISTENCE OF WEAK SOLUTIONS FOR THE KIRCHHOFF-TYPE EQUATION WITH MIXED BOUNDARY CONDITIONS IN VARIABLE EXPONENT SOBOLEV SPACE http://eastwestmath.org/index.php/ewm/article/view/516 <p class="p1">In this paper, we consider the Kirchhoff-type equation for a class of</p> <p class="p1">nonlinear operators containing p(·)-Laplacian and mean curvature oper-</p> <p class="p1">ator with mixed boundary conditions. More precisely, we are concerned</p> <p class="p1">with the problem under the Dirichlet condition on a part of the boundary</p> <p class="p1">and the Steklov boundary condition on an another part of the boundary.</p> <p class="p1">We show the existence of one, two and infinitely many nontrivial weak</p> <p class="p1">solutions of the equation according to the conditions on given functions.</p> Junichi Aramaki Copyright (c) 2025 East West Math http://eastwestmath.org/index.php/ewm/article/view/516 Mon, 28 Jul 2025 00:00:00 +0800 BASIC PROPERTY OF GENERALIZED COMPLETELY MULTIPLICATIVE FUNCTIONS http://eastwestmath.org/index.php/ewm/article/view/518 <p class="p1">An arithmetic function f is said to be completely multiplicative if</p> <p class="p1">f (1) = 1 and f (mn) = f (m)f (n) for all positive integers m and n.</p> <p class="p1">In this paper, we define that an arithmetic function f is a generalized</p> <p class="p1">completely multiplicative function if f (1) = 1 and there is a completely</p> <p class="p1">multiplicative function f<span class="s1">b </span>such that f (mn) = f (m)<span class="s1">f</span><span class="s2">b </span><span class="s1">(n)</span>f (n)<span class="s1">f</span><span class="s2">b </span><span class="s1">(m) </span>for all</p> <p class="p1">positive integers m and n. We consider some basic structure properties of</p> <p class="p1">these functions. The functions v(n) = n<span class="s1">n </span>and ExpD are examples of gen-</p> <p class="p1">eralized completely multiplicative functions, where D is the arithmetic</p> <p class="p1">derivative.</p> Pentti Haukkanen Copyright (c) http://eastwestmath.org/index.php/ewm/article/view/518 Mon, 28 Jul 2025 15:34:00 +0800 SOME RESULTS ON LOCAL COHOMOLOGY MODULES WITH RESPECT TO A PAIR OF IDEALS http://eastwestmath.org/index.php/ewm/article/view/519 <p class="p1">We introduce some results for the local cohomology modules with</p> <p class="p1">respect to a pair of ideals (I, J), which is a generalization of the concept</p> <p class="p1">of local cohomology modules with respect to an ideal I.</p> C.H. Tognon Copyright (c) http://eastwestmath.org/index.php/ewm/article/view/519 Mon, 28 Jul 2025 15:49:12 +0800 FORECASTING OF CHANGES IN SALINITY INTRUSION IN THE VIETNAMESE MEKONG DELTA BY THE COMBINED MODEL OF LSTM (Long Short-Term Memory) AND SRM (Sinusoidal Regression Model) http://eastwestmath.org/index.php/ewm/article/view/520 <p class="p1">The salinity intrusion in the Vietnamese Mekong Delta (VMD) has become</p> <p class="p1">more complex and temporally heterogeneous. This could seriously threaten the</p> <p class="p1">livelihoods of local residents and agricultural activities. Therefore, the research</p> <p class="p1">was conducted by using a combined model of LSTM (Long Short-Term Mem-</p> <p class="p1">ory) and SRM (Sinusoidal Regression Model) to assess the trends and anomalies</p> <p class="p1">of salinity intrusion, with a series of data collected from main stations in the VMD</p> <p class="p1">in the year of 2021. The findings showed that the combined model exhibited high</p> <p class="p1">predictive (R<span class="s1">2 </span>= 0.9299, M SE = 2.0861, and M AP E = 0.1276) in fore-</p> <p class="p1">casting the increasing and decreasing trends of salinity intrusion and effectively</p> <p class="p1">detecting anomalous variations. Consequently, these results could be helpful to</p> <p class="p1">policymakers in predicting and responding to future salinity intrusion and to likely</p> <p class="p1">widespread implications for other regions impacted by saline intrusion.</p> Uyen T. Huynh Copyright (c) 2025 East West Math http://eastwestmath.org/index.php/ewm/article/view/520 Mon, 28 Jul 2025 15:58:21 +0800 A VISION OF THE THEORY OF LOCAL COHOMOLOGY MODULES http://eastwestmath.org/index.php/ewm/article/view/521 <p class="p1">This paper is concerned with the relation between the theory of local</p> <p class="p1">cohomology modules of a module, defined by an ideal, and associated</p> <p class="p1">prime ideals of a module.</p> Carlos Henrique Tognon Copyright (c) 2025 East West Math http://eastwestmath.org/index.php/ewm/article/view/521 Mon, 28 Jul 2025 16:02:39 +0800