Maximum bound principle (MBP) is an important property for a large class of semilinear parabolic equations, in the sense that time-dependent solution equation with appropriate initial and boundary conditions nonlinear operator preserves all time uniform pointwise absolute value. It has been challenging problem on how to design unconditionally MBP-preserving high-order accurate time-stepping sch...

Abstract In this paper, we first define a primitive protocol of secure multiparty computations to privately compute the logic operator “OR” (SMC_OR). Accordingly, design feasible quantum SMC_OR by using single photons, which can achieve information-theoretical security in semi-honest model. Furthermore, adopt proposed solve an interesting but important privacy-preserving problem, i.e., finding ...

We will extend Ostrowki’s theorem from Q to the quadratic field Q(i). On Q, every nonarchimedean absolute value is equivalent to the p-adic absolute value for a unique prime number p, and the archimedean absolute values are all equivalent to the usual absolute value on Q. We will see a similar thing happens in Q(i): any non-archimedean absolute value is associated to a prime in Z[i] (unique up ...

Functions preserving Loewner positivity when applied entrywise to positive semidefinite matrices have been widely studied in the literature. Following the work of Schoenberg [Duke Math. J. 9], Rudin [Duke Math. J. 26], and others, it is well-known that functions preserving positivity for matrices of all dimensions are absolutely monotonic (i.e., analytic with nonnegative Taylor coefficients). I...

in this paper, we give a characterization of strongly jordan zero-product preserving maps on normed algebras as a generalization of  jordan zero-product preserving maps. in this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly jordan zero-product preserving maps are completely different. also, we prove that the direct p...