Let R be a ring with an endomorphism σ and a σ-derivation δ. R is called (σ, δ)-Baer (resp. (σ, δ)-quasi-Baer, (σ, δ)-p.q.-Baer, (σ, δ)-p.p.) if the right annihilator of every right (σ, δ)-set (resp., (σ, δ)-ideal, principal (σ, δ)-ideal, (σ, δ)-element) of R is generated by an idempotent of R. In this paper, for a given Ore extension A = R[x; σ, δ] of R, the following properties are investigated: If R is a σ-rigid ring in which σ and δ commute, then (1) R is (σ, δ)-Baer if and only if R is (σ, δ)-quasi-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-quasi-Baer; (2) R is (σ, δ)-p.p. if and only if R is (σ, δ)-p.q.-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.p. if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.q.-Baer.

We establish multiplicity results for positive solutions to the Schrödinger-type singular positone problem: -∆u + V (x)u = λf(u) in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in ℝ^N, N > 2, λ is a positive parameter, V ∈ L^∞(Ω) and f : [0, ∞) → (0, ∞) is a continuous function. In particular, when f is sublinear at infinity we discuss the existence of at least three positive solutions for a certain range of λ. The proofs are mainly based on the sub- and supersolution method.

This paper is concerned with the optimal control problem associated to the self-organizing target detection model in 1D domains. That is, we show the global existence of weak solution and the existence of optimal control.

In this paper, we study singular Dirichlet boundary value problems involving ϕ-Laplacian. Using fixed point index theory, the existence of positive solutions is established under the assumption that the nonlinearity f = f(u) has a positive falling zero and is either superlinear or sublinear at u = 0.

Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (φ, ξ, η, g) in a complex space form M_n+1(c). We denote by R_ξ the structure Jacobi operator with respect to the structure vector field ξ and by ${\bar{r}}$ the scalar curvature of M. Suppose that R_ξ is φ∇_ξξ-parallel and at the same time the third fundamental form t satisfies dt(X, Y) = 2θg(φX, Y) for a scalar θ(≠ 2c) and any vector fields X and Y on M. In this paper, we prove that if it satisfies R_ξφ = φR_ξ, then M is a Hopf hypersurface of type (A) in M_n+1(c) provided that ${\bar{r}-2(n-1)c}$ ≤ 0.

This paper is based on Yanbian University's physical test data, and uses statistical analysis methods to study the relationship between college students' physical test scores to promote college physical education. Firstly, using gender as categorical variables, we conduct a general analysis of students in different majors and different grades, and obtain the advantages and disadvantages of male and female college students; then we use Decision Trees and Random Forest algorithms to conduct modeling analysis to provide valuable suggestions for relevant departments of the university. the aiming of this research analyzing about the undergraduates physical test is that giving universities the targeted suggestions to improve the college graduate rate and promote the overall development of higher education, lay the foundation for achieving universal health.

Recently, an LWE-based commitment scheme is proposed. Their construction is statistically hiding as well as computationally binding. On the other hand, the construction of related zero-knowledge protocols is left as an open problem. In this paper, we present zero-knowledge protocols with hardness based on the LWE problem. we show how to instantiate efficient zero-knowledge protocols that can be used to prove linear and sum relations among these commitments. In addition, we show how the variant of LWE, spLWE problem, can be used to instantiate efficient zero-knowledge protocols.

In this paper, we consider a quadratic matrix equation Q(X) = AX² + BX + C = 0 where A, B, C ∈ ℝ^n×n. A new approach is proposed to find solutions of Q(X), using the novel structure of the information processing system. We also present some numerical experimetns with Artificial Neural Network.

In this paper, we discuss the relationship between doubly-pointed Heegaard diagrams of (1, 1)-knots in lens spaces and Dunwoody 3-manifolds, and then give explicit representations of n-fold cyclic branched coverings of all (1, 1)-knots in S³ up to 10 crossings in Rolfsen's knot table as Dunwoody 3-manifolds.

We obtain interior regularity estimates in the weighted Orlicz spaces for viscosity solutions of fully nonlinear uniformly parabolic equations u_t - F(D² u, x, t) = f(x, t) in Q₁ under relaxed structure conditions on the nonlinear operator F.