In this presented article, we have exemplified and studied the Fr?chet differentiation of nonlinear operators between neutrosophic normed spaces as a generalization of notions given [34] and introduced nonlinear theory of neutrosophic bounded operators by introducing chain rule and some algebraic properties of Fr?chet differentiation of operators between neutrosophic normed spaces.

Let ? = (G, ?) be a T-gain graph. In this note we show that ? has one positive and negative eigenvalues if and only if it is switching equivalent to a balanced complete bipartite graph or complete tripartite with special weights. In addition, we found some lower bounds for the energy of a T-gain graph.

This paper mainly discuss eight kinds of equivalent characterizations of an M-fuzzifying topological closure operator cl: 2X ? MX, an M-fuzzifying topological interior operator int: 2X ? MX, and an M-fuzzifying topological derived operator der: 2X ? MX, in which M is a completely distributive De Morgan algebra. As its applications, we give the fuzzy constructions of M-fuzzifying topological operators cld, intd, derd induced by an M-fuzzifying pseudo metric d in the sense of Morsi?s fuzzy metric and prove that the continuity between M-fuzzifying topological operator spaces and M-fuzzifying pseudo metric spaces is maintained. Finally, we show that the M-fuzzifying topological T induced by d is exactly the M-fuzzifying topological induced by cld, intd and derd. Namely, Td = Tcld = Tintd = Tderd.

In the present paper, we developed a new explicit Milstein-type integrator for stiff SDEs. Theoretically, we indicate that the scheme converges to the true value with a strong order of 1.0. For linear scalar SDE, the asymptotic mean square stability of our method is investigated. For all time steps, we prove that the presented integrator is asymptotically mean square stable. In addition, the A-stability and L-stability of the scheme was discussed in the mean square sense. For dimension two of the submitted scheme, the asymptotic mean square stability of two test systems has been analyzed. Numerical simulations confirm the theoretical results.

Applying the fixed point theorem, we offer the existence of solutions of an infinite system of mixed Volterra-Fredholm type of nonlinear integral equations in the sequence space c0. To further demonstrate the given existence result, we provided examples.

In this paper, we introduce matrix weighted Bourgain-Morrey spaces and obtain two sufficient conditions for precompact sets in matrix weighted Bourgain-Morrey spaces. We prove that the dyadic average operator is bounded on some matrix weighted Bourgain-Morrey spaces. With this result, we obtain the necessity for precompact sets in some matrix weighted Bourgain-Morrey spaces. The results are new even for the unweighted Bourgain-Morrey spaces.

In this study, we construct bivariate Bernstein-Kantorovich polynomials which reproduce exponential function and investigate some approximation results for these operators. We use the test functions to prove Korovkin-type theorem. Then we obtain the rate of convergence by means of the modulus of continuity. We demonstrate the Voronovskaya-type theorem for the newly constructed operator. In the last section, we represent some illustrative graphics to show the convergence of the constructed operators and we give some numerical results.

In this paper, we mainly prove the boundedness of commutators generated by Hardy type operator and p-adic mixed central campanato functions in p-adic mixed central Morrey spaces, and give some characterizations of p-adic central mixed campanato spaces.

This article delves into the investigation of simplex codes of types ?, ?, and ? over the ring Z3Z6. It examines the fundamental properties of these codes, including their covering radius, association schemes, and practical applications in multi-secret sharing schemes. The covering radius analysis sheds light on the error-correcting capabilities of Z3Z6-simplex codes, crucial for reliable communication systems. Additionally, association schemes for Z6-simplex codes provide insights into efficient encoding and decoding strategies, enhancing their performance in various applications. Furthermore, the development of a multi-secret sharing scheme based on these codes highlights their versatility beyond traditional error correction, offering promising avenues for secure multi-party communication and data storage. This explo-ration of simplex codes over Z3Z6 not only contributes to theoretical coding theory but also opens up new opportunities in practical cryptography, advancing the realm of secure information exchange protocols.

Let A be a unital C*-algebra with unit e and let ? ? [0, 1]. We introduce the concept of the ?-weighted contraharmonic mean of two positive definite elements a and b of A by C?(a, b) := 2 ((1 ? ?)a + ?b)?((1 ? ?)a?1 + ?b?1)?1. When ? ? (0, 1), we show that C?(a, b) = max x+y=e {2(1 ? ?)a ? (1 ? ?)?1x*ax + 2?b ? ??1y*by}, and then apply it to present some properties of this weighted mean.