Related papers: A minimal closed-form solution to the conic based …
We consider nonlinear Schr\"odinger equations on flat tori satisfying a simple and explicit Diophantine non-degeneracy condition. Provided that the nonlinearity contains a cubic term, we prove the almost global existence and stability of…
The purposes of this paper are to classify lower triangular forms and to determine under what conditions a nonlinear system is equivalent to a specific type of lower triangular forms. According to the least multi-indices and the greatest…
We consider representations of tensors as sums of decomposable tensors or, equivalently, decomposition of multilinear forms into one--forms. In this short note we show that there exists a particular finite strongly orthogonal decomposition…
The paper deals with positive radial solutions to a nonlinear elliptic equation with singular and decaying potential, for which several existence and nonexistence results are known, resting upon suitable compatibility conditions between the…
We describe and analyze an interior-point method to decide feasibility problems of second-order conic systems. A main feature of our algorithm is that arithmetic operations are performed with finite precision. Bounds for both the number of…
A method for solving cyclic block three-diagonal systems of equations is generalized for solving a block cyclic penta-diagonal system of equations. Introducing a special form of two new variables the original system is split into three…
In this paper we discuss quantitative (pointwise) decay estimates for solutions to the 3D cubic defocusing Nonlinear Schr\"odinger equation with various initial data, deterministic and random. We show that nonlinear solutions enjoy the same…
We are concerned with the dependence of the lowest positive eigenvalue of the Dirac operator on the geometry of rectangles, subject to infinite-mass boundary conditions. We conjecture that the square is a global minimiser both under the…
We show the existence of a weak solution of a semilinear elliptic Dirichlet problem on an arbitrary open set. We make no assumptions about the open set, very mild regularity assumptions on the semilinearity, plus a coerciveness assumption…
This work investigates the fundamental properties of the degenerate preconditioned resolvent under restricted monotonicity. We extend key notions of non-expansiveness and demiclosedness to the degenerate case. By deriving an explicit…
We study families of triangles that are inscribed in a fixed circle and circumscribed about a central conic, extending the classical Chapple--Euler relation within the framework of Poncelet geometry. We establish several geometric…
We present a criterion when six points chosen on the sides of a triangle belong to the same conic. Using this tool we show how the two geometrical gems - celebrated Poncelet's theorem of projective geometry and incredible Morley's theorem…
In this article we present a formula for the plurigenera of minimal models of nondegenerate toric hypersurfaces, which is valid in arbitrary dimension and which expresses these invariants through lattice points on the Fine interior. From…
An effective method for generating linear equations of maximal symmetry in their much general normal form is obtained. In the said normal form, the coefficients of the equation are differential functions of the coefficient of the term of…
We present an efficient framework for solving algebraically-constrained global non-convex polynomial optimization problems over subsets of the hypercube. We prove the existence of an equivalent nonlinear reformulation of such problems that…
In this paper we investigate the deformation of cylindrical linearly elastic shells using the Koiter model. We formulate and solve the relaxed Saint-Venant's problem for thin cylindrical tubes made of isotropic and homogeneous elastic…
In this paper, we establish the well-posedness of Cauchy problems for weak solutions to second-order degenerate parabolic equations with a non-smooth, time-dependent degenerate elliptic part that includes both bounded and unbounded…
We develop a new interior-point algorithm for solving multiconic optimization problems using the parabolic target space approach. The feasible cone in these problems is composed as a direct product of many small-dimensional cones. Our…
In this paper we consider nonlinear parabolic systems with elliptic part which can be also degenerate. We prove optimal error estimates for smooth enough solutions. The main novelty, with respect to previous results, is that we obtain the…
A new one-parameter family of iterative method for solving nonlinear equations is constructed and studied. Two variants, both with cubic convergence, are developed, one for finding simple zeros and other for multiple zeros of known…