On Hilbert polynomial of certain determinantal ideals by Shrinivas G. Udpikar

“…A part of the second fundamental theorem of Invariant Theory says that the ideal I[p+1] in K[X], generated by (p+1) by (p+1) minors of X is prime. …”
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Research of the Similarity Experiment Mechanism of Face Gear Transmission System Under High Energy Flow Density by Wang Yanzhong, Tang Wen, Liu Yang, Chen Yanyan, Liu Yuanpeng

“…In order to simplify the experiment condition and reduce test cost,the similarity theory of the tooth root bending stress and vibration acceleration is obtained based on the dimensional analysis theorem. The tooth root bending stress and vibration acceleration of face gear under high- speed and heavy- load conditions are measured by the experiment. …”
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New Existence Results for Nonlinear Fractional Integrodifferential Equations by Lahcen Ibnelazyz, Karim Guida, Khalid Hilal, Said Melliani

“…In particular, we make use of the Banach contraction mapping principle and Krasnoselskii’s fixed point theorem under some weak conditions. Moreover, two illustrative examples are studied to support the results.…”
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Continuous in time bubble decomposition for the harmonic map heat flow by Jacek Jendrej, Andrew Lawrie, Wilhelm Schlag

“…This is deduced as a corollary of our main theorem, which shows that the solution approaches the family of multi-bubble configurations in continuous time.…”
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Order and Chaos in a Prey-Predator Model Incorporating Refuge, Disease, and Harvesting by Dahlia Khaled Bahlool, Huda Abdul Satar, Hiba Abdullah Ibrahim

“…Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. …”
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Waves due to initial disturbances at the inertial surface in a stratified fluid of finite depth by Prity Ghosh, Uma Basu, B. N. Mandal

“…The techniques of Laplace transform in time and either Green's integral theorem or Fourier transform have been utilized in the mathematical analysis to obtain the form of the inertial surface in terms of an integral. …”
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Optimality Conditions and Scalarization of Approximate Quasi Weak Efficient Solutions for Vector Equilibrium Problem by Yameng Zhang, Guolin Yu, Wenyan Han

“…Finally, by using Tammer’s function and the directed distance function, the scalarization theorems of the approximate quasi weak efficient solutions of the VEP are proposed.…”
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Some Modified Fixed Point Results in V-Fuzzy Metric Spaces by Vishal Gupta, Manu Verma, Mohammad Saeed Khan

“…This proved fixed point theorem in V-fuzzy metric space employing the effectiveness of E.A. property and CLRg property. …”
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A New Hybrid Algorithm for Convex Nonlinear Unconstrained Optimization by Eman T. Hamed, Huda I. Ahmed, Abbas Y. Al-Bayati

“…We tend to conjointly prove a replacement theorem to make sure global convergence property is underneath some given conditions. …”
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On Kalman Smoothing for Wireless Sensor Networks Systems with Multiplicative Noises by Xiao Lu, Haixia Wang, Xi Wang

“…The Kalman smoothers which include Kalman fixed-interval smoother, Kalman fixedlag smoother, and Kalman fixed-point smoother are given by solving Riccati equations and Lyapunov equations based on the projection theorem and innovation analysis. An example is also presented to ensure the efficiency of the approach. …”
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A Convolution-Based Shearlet Transform in Free Metaplectic Domains by Tarun K. Garg, Waseem Z. Lone, Firdous A. Shah, Hatem Mejjaoli

“…Besides obtaining the orthogonality relation, inversion formula, and range theorem, we also study the homogeneous approximation property for the proposed transform. …”
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Modelling and Regularity of Nonlinear Impulsive Switching Dynamical System in Fed-Batch Culture by Lei Wang

“…In order to overcome the discontinuities of the system, the Skorohod topology is induced and a specific form of λ is constructed to prove the main theorem. Additionally, a numerical simulation is carried out to show that the proposed system can describe the fed-batch culture properly and the essential difference with the previous work.…”
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The Normalized Laplacians, Degree-Kirchhoff Index, and the Complexity of Möbius Graph of Linear Octagonal-Quadrilateral Networks by Jia-Bao Liu, Qian Zheng, Sakander Hayat

“…In this paper, starting from the decomposition theorem of polynomials, we infer that the normalized Laplacian spectrum of MQn8,4 can be determined by the eigenvalues of two symmetric quasi-triangular matrices ℒA and ℒS of order 4n. …”
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On efficient iterative schemes for finding all solutions of non-linear engineering problems by Mudassir Shams, Nasreen Kausar

“…The main aim of this effort is to develop an efficient higher-order simultaneous computer approach capable of computing all solutions concurrently. The convergence theorem analysis indicates that the scheme has a local convergence order of 10. …”
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Some Developments in the Field of Homological Algebra by Defining New Class of Modules over Nonassociative Rings by Asima Razzaque, Inayatur Rehman

“…We have proved the projective basis theorem for LA-modules. Also, split sequences in projective and injective LA-modules are discussed with the help of various propositions and theorems.…”
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A Degree Theory for Compact Perturbations of Monotone Type Operators and Application to Nonlinear Parabolic Problem by Teffera M. Asfaw

“…Consequently, new existence theorems are provided. The existence theorem due to Asfaw and Kartsatos is improved. …”
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Global well-posedness of 2D incompressible Navier–Stokes–Darcy flow in a type of generalized time-dependent porosity media by Linlin Tan, Bianru Cheng

“…To address this issue, we employ the classical Trace Theorem. Such space-time variable coupled systems are crucial for understanding underground fluid flow.…”
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Topological Dual Systems for Spaces of Vector Measure p-Integrable Functions by P. Rueda, E. A. Sánchez Pérez

“…We show a Dvoretzky-Rogers type theorem for the adapted version of the q-summing operators to the topology of the convergence of the vector valued integrals on Banach function spaces. …”
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Positive Solutions for Third-Order Nonlinear p-Laplacian m-Point Boundary Value Problems on Time Scales by Fuyi Xu

“…We obtain the existence of positive solutions by using fixed-point theorem in cones. The conclusions in this paper essentially extend and improve the known results.…”
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A Strong Law of Large Numbers for Random Sets in Fuzzy Banach Space by R. Ghasemi, A. Nezakati, M. R. Rabiei

“…Since many years ago, limited theorems have been expressed and proved for fuzzy random variables, but despite the uncertainty in fuzzy discussions, the nonfuzzy metric space has been used. …”
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