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Abstract: Abstract Let \(A, B, D, E \in [-1,1]\) and let p(z) be an analytic function with fixed initial coefficient defined in the open unit disk. Conditions on A, B, D, and E are determined so that \(1+ \alpha z p'(z)\) being subordinated to \((1+Dz)/(1+Ez)\) implies that p(z) is subordinated to \((1+Az)/(1+Bz)\) and other similar implications involving \(1+ \alpha z p'(z)/p(z)\) , \(\alpha p^2(z) + \lambda z p'(z) \) , \( \alpha p(z) + (1-\alpha ) p^2(z) + \lambda z p'(z)\) , and \( (1-\alpha ) p(z) + \alpha \left( 1+ z p'(z)/p(z) \right) \) . Also, sufficient conditions for Janowski starlikeness with fixed second coefficient are obtained. PubDate: 2022-11-25

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Abstract: Abstract In this article, we analyze Bianchi type-II, VIII and IX spatially homogeneous and anisotropic space–times in the background of f(R) theory of gravity with a strange quark matter attached to a string cloud. Here, both in the presence and absence of cosmic strings, we have achieved the deterministic solution of the field equations. To solve the field equations we use (i) the shear scalar \(\sigma \) is proportional to the expansion scalar \(\vartheta \) which leads to a relation between metric potentials (ii) a power–law relation between the scalar function F(R) of the theory and average scale factor a(t) of the Universe and (iii) a special form of the average scale factor obtain from the time-varying deceleration parameter. Furthermore, all the models obtained and presented here are expanding and accelerating. Also, we have discussed some of the dynamical parameters of obtained models through graphical representation which is significant in the discussion of modern cosmology. PubDate: 2022-11-15

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Abstract: Abstract In this paper, we propose the idea of a root-mean-square-threshold or RMS-threshold for the Pythagorean fuzzy soft set (PFSS). In light of this new concept, we characterized the RMS-level soft set in order to provide additional rationale for decision-making using Pythagorean fuzzy soft information. Moreover, we propose the concept of a weighted Pythagorean fuzzy soft set (WPFSS) with two-tuple weights and talk about its utility for decision-making issues. We initially stretch out the RMS approach to diagnosing numerous patients with different diseases with WPFSS data. PubDate: 2022-11-11

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Abstract: Abstract In this paper, we study the biwarped product submanifold in locally nearly metallic Riemannian manifold. We construct a non trivial example of a biwarped product submanifold in metallic Riemannian manifold. Moreover, we discuss a necessary and sufficient condition for such submanifolds to be locally trivial. Finally, we set up an inequality in locally nearly metallic Riemannian manifold for the second fundamental form with respect to some conditions. We also investigate the equality case. PubDate: 2022-10-26

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Abstract: Abstract In this article, we study the problem of the existence and nonexistence of warping function associated with constant scalar curvature on pseudo-Riemannian Poisson warped product space under the assumption that fiber space has constant scalar curvature. We characterize the warping function on Einstein Poisson warped space by taking the various dimensions of base space B (i.e; (1). \(dim B=1,\) (2). \(dimB\ge 2\) ). PubDate: 2022-09-20

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Abstract: Abstract A new bivariate distribution that has the potential to describe simultaneous occurrences of random processes with outcomes of the form \(\left(x,y\right)\) , where \(x<y\) is derived. It is a five-parameter upper-diagonal bivariate epsilon distribution for modeling ordered random variables. The shapes of the density and contour plots show the new distribution possesses the potential for modeling simultaneous random variables such as minimum and maximum temperatures, systolic and diastolic blood pressures, weight of mothers and babies at birth, length and breadth of oval shapes. Its properties, such as conditional distributions, univariate marginal distributions and the extreme-value distributions are derived. It is generalized in a multivariate form. It is applied to minimum and maximum temperatures data from Yola. The parameter estimates provides good fit. The conditional expectation of the maximum temperature requirements for 13 crops to thrive in Yola are estimated using these parameter values. The conditioning is taken over minimum temperature for these crops to grow in the Sahel region. For most of these crops, the values obtained are outside the optimal temperature range for growth and yield performance. This portends discouragement in farming and investment in agriculture. It is therefore suggested that more research efforts should be geared towards improved seedling for these crops. This will enhance earnings of African peasant farmers and guarantee food security. PubDate: 2022-09-16

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Abstract: Abstract In this paper by an application of Krasnoselskii’s fixed point theorem, we establish the existence of infinitely many positive radial solutions to the iterative system of nonlinear elliptic equations of the form $$\begin{aligned} \begin{aligned}&\varDelta { v_{\mathtt {j}}}+\frac{(N-2)^2r_0^{2N-2}}{\vert \mathtt {x}\vert ^{2N-2}}v_\mathtt {j}+\mathtt {Q}(\vert \mathtt {x}\vert )\mathtt {g}_{\mathtt {j}}( v_{\mathtt {j}+1})=0,~~\mathtt {x}\in \varOmega ,\\&\quad v_{\mathtt {j}}\vert _{\partial \varOmega }=0,~ \lim _{\vert \mathtt {x}\vert \rightarrow \infty }v_{\mathtt {j}}(\mathtt {x})=0, \end{aligned} \end{aligned}$$ where \(\mathtt {j}\in \{1,2,3,\ldots ,m\},\) \( v_1= v_{m+1},\) \(\varDelta v=\mathtt {div}(\nabla v),\) \(N>2,\) \(0<r_0<\pi /2,\) \(\varOmega =\{ v\in \mathbb {R}^N ~\vert v\vert >r_0\},\) \(\mathtt {Q}=\prod _{i=1}^{n}\mathtt {Q}_i,\) each \(\mathtt {Q}_i:(r_0,+\infty )\rightarrow (0,+\infty )\) is continuous, \(r^{N-1}\mathtt {Q}\) is integrable, may have singularities, and \(\mathtt {g}_\mathtt {j}:[0,+\infty )\rightarrow \mathbb {R}\) is continuous. PubDate: 2022-09-13 DOI: 10.1007/s13370-022-01027-3

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Abstract: Abstract In this paper we present a construction for partial order in T[X, Y] which is called the ternary semigroup of mappings, derived from the partial orders defined in X and Y. Mainly we study various lattice structures in T[X, Y]. The last section deals with the lattice isomorphism problems and the notion of partially ordered ternary semigroup in T[X, Y]. PubDate: 2022-09-07 DOI: 10.1007/s13370-022-01028-2

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Abstract: In this paper, the existence of infinitely many positive solutions for an iterative system of singular fractional order boundary value problems having increasing homeomorphism and positive homomorphism operator (IHPHO) with Rieman–Stieltjes integral boundary conditions are discussed. The arguments are discussed via Hölder’s inequality and Krasnoselskii’s cone fixed point theorem in a Banach space. Finally, some examples are included to ensure the abstract results. PubDate: 2022-09-07 DOI: 10.1007/s13370-022-01026-4

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Abstract: Abstract In this article, we define the notion of \(\Gamma \) -near-rings on weak nearness approximation spaces and explain some of the concepts and definitions. Then, we study some basic properties of \(\Gamma \) -nearness near-rings. \(\Gamma \) -nearness near-rings are different from \(\Gamma \) -nearness rings and \(\Gamma \) -nearness semirings because the set of \(\Gamma \) does not have to be grouped in \(\Gamma \) -nearness near-rings. Because of this, some properties defined in \(\Gamma \) -nearness rings and \(\Gamma \) -nearness semirings show some changes in \(\Gamma \) -nearness near-rings. PubDate: 2022-08-24 DOI: 10.1007/s13370-022-01024-6

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Abstract: Abstract In this paper, we consider an h-almost Ricci-Bourguignon soliton and we provide some useful formulas of structure for this soliton. Then for an application of these formulas we show that a noncompact, complete nontrivial gradient h-Ricci-Bourguignon soliton is isometric to Euclidean space and a compact nontrivial h-almost Ricci-Bourguignon soliton is isometric to a Euclidean sphere with some conditions. PubDate: 2022-08-15 DOI: 10.1007/s13370-022-01025-5

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Abstract: Abstract In the present paper, the rainfall forecast information is analyzed using model and density based clustering algorithms and good model is fitted by using structural equation modelling and artificial neural networks. Shapiro-Wilk normality test for Water Level, In Flow, Period, Rainfall are 0.7694, 0.2388, 0.7651, 0.4382 respectively with same p-value \(< 2.2 \times 10^{-16}\) . It shows that all are highly significantly non-normal. For the percentage on the Water Level, the variances were similar for Yes and No (Rainfall), significantly different, but for inflow the variances were not significantly different in the two groups, whereas for the period, the variances were similar for Yes and No (Rainfall), significantly different. The number of observations in the clusters 0 to cluster 9 are 18, 64, 39, 20, 19, 88, 41, 41, and 36. Here, cluster 0 represents the outlier in which we have 19 observations out of 366 observations in model based clustering. Furthermore, DBSCAN performs better for these data sets and can identify the correct set of clusters compared to k-means algorithms. The Fit indices for our structural equation model in which most of them show that our model is good to fit except the absolute type with Chi-square \(\left( \chi ^2\right) \) . Finally, we use 10 fold cross validated MSE for the linear model. The cv.glm is 0.1252 and it is shown in the box plot. PubDate: 2022-08-15 DOI: 10.1007/s13370-022-01023-7

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Abstract: Abstract In this study, by using Lucas polynomials, subordination and q-analogue of Noor integral operator, we will introduce an interesting new class \(Q^{q,\mu }(\tau ,\alpha ;x)\) of bi-univalent functions. Also we will obtain (P, Q)-Lucas polynomial coefficient estimates and Fekete–Szegö inequalities for this new class. PubDate: 2022-08-06 DOI: 10.1007/s13370-022-01016-6

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Abstract: Abstract In this paper, we provide a comprehensive numerical analysis of Fourier-type pseudo-spectral methods applied to the semilinear Klein–Gordon equation (KGE) with smooth potentials. It is shown explicitly that for KGE potentials of finite regularity, the convergence rate of such schemes is at most algebraic and is controlled solely by the regularity of input data and the associated KGE potential. It turns out that the spectral convergence rate can only occur for KGE models with entire potentials. In the latter case, an explicit quantitative error estimate, characterizing spectral convergence rate, is provided. The paper is concluded with several computational examples supporting our theoretical analysis. PubDate: 2022-08-06 DOI: 10.1007/s13370-022-01021-9

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Abstract: Abstract In this paper, we consider a nonlinear neutral Caputo nabla fractional difference equation. In the analysis, we use the nabla discrete Mittag–Leffler functions to transform the equation into an applicable equation. By applying Krasnoselskii’s fixed point theorem, sufficient conditions for the existence of solutions are established, also the uniqueness of the solution is given by the Contraction mapping principle. In addition, we give interesting results for stability and asymptotic stability. To examine the validity of our findings, a concrete example with numerical simulation diagrams is analyzed. Our main results extend and generalize the results that are obtained in [12]. PubDate: 2022-07-26 DOI: 10.1007/s13370-022-01020-w

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Abstract: Abstract In this paper various properties of nilpotent and controllable intuitionistic fuzzy matrix are explored. We develop an algorithm for controllable and nilpotent intuitionistic fuzzy matrices and reduce a controllable intuitionistic fuzzy matrix to canonical form using that algorithm. PubDate: 2022-07-26 DOI: 10.1007/s13370-022-01019-3

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Abstract: Abstract Let \(\overline{B}_{\ell }(n)\) denote the number of \(\ell -\) regular overpartition pairs of n. In this paper, we find some Ramanujan like congruences and infinite families of congruences for \(\overline{B}_{\ell }(n)\) for \(\ell \in \{3,4,5,8\}\) . For example, for \(n \ge 0\) and \(\alpha \ge 0\) , \(\overline{B}_{3}(4^{\alpha +1}(6n+5))\equiv 0\pmod {9}\) , \(\overline{B}_{3}(12n+10)\equiv 0\pmod {9}\) , \(\overline{B}_{5}(4n+3)\equiv 0\pmod {8}\) and \(\overline{B}_{8}(16n+12)\equiv 0\pmod {16}\) . PubDate: 2022-07-19 DOI: 10.1007/s13370-022-01018-4

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Abstract: Abstract The aim of this paper is to apply bipolar-valued fuzzy sets in \({\mathcal {L}}{\mathcal {A}}\) -semigroup theory. We introduce the concept of bipolar-valued fuzzy quasi-semiprime and bipolar-valued fuzzy semiprime ideals in \({\mathcal {L}}{\mathcal {A}}\) -semigroups. In addition, we also characterize bipolar-valued fuzzy quasi-semiprime ideal by the properties of these bipolar-valued fuzzy points. Moreover, we investigated relationships between bipolar-valued fuzzy quasi-semiprime ideals and bipolar-valued fuzzy semiprime ideals. Finally, several characterizations of bipolar-valued fuzzy quasi-semiprime ideal by the properties of \(\left( t,t\right) \) -cut sets are given. PubDate: 2022-07-13 DOI: 10.1007/s13370-022-01009-5

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Abstract: Abstract The main ambition proposed in this article is to provide new fixed point results for triangular \(\alpha \) -orbital admissible contractions via some auxiliary and simulation functions in the frame of extended b-metric-like spaces. As an application, we prove the existence of a unique solution for a nonlinear fractional differential equation with exponential weighted integral boundary conditions via the generalized proportional fractional derivative of Caputo type with order \(\beta \in (n-1, n]\) . Further, we demonstrate the usability of our results through several examples. PubDate: 2022-07-12 DOI: 10.1007/s13370-022-01017-5