A syntactically-driven approach to indefiniteness, specificity and anti-specificity in Romance

In this paper we present an original approach to analyze the compositionality of indefinite expressions in Romance by investigating the relevance of their syntactic distribution in relation to their meaning. This approach has the advantage of allowing us to explore the question of how syntactic structure can determine the meaning of different forms of indefiniteness. To that end, we postulate a common derivation for bare plurals, bare mass and de phrases, whereby an abstract operator de is adjoined to definite determiners and shifts entities into property-type expressions. Quantificational specificity is proposed to be derived from a syntactic structure in which weak quantifiers select for indefinite de-phrases, no matter whether de is overt at Spell-Out or not; these quantifiers turn properties into generalized quantifiers. The anti-specificity meaning of some indefinites is derived by adjoining in the syntactic structure an abstract operator alg that encodes the speaker’s epistemic state of ignorance to a quantifier encoded for specificity, and it turns a generalized quantifier into a modified generalized quantifier. The paper also brings some general predictions on how indefiniteness is expressed in Romance, as it provides extensive support from five Romance languages: Brazilian Portuguese, Catalan, French, Italian and Spanish.

On Compressed Resolvents of Schrödinger Operators with Complex Potentials

The compression of the resolvent of a non-self-adjoint Schrödinger operator $$-\Delta +V$$ - Δ + V onto a subdomain $$\Omega \subset {\mathbb {R}}^n$$ Ω ⊂ R n is expressed in a Kreĭn–Naĭmark type formula, where the Dirichlet realization on $$\Omega $$ Ω , the Dirichlet-to-Neumann maps, and certain solution operators of closely related boundary value problems on $$\Omega $$ Ω and $${\mathbb {R}}^n\setminus {\overline{\Omega }}$$ R n \ Ω ¯ are being used. In a more abstract operator theory framework this topic is closely connected and very much inspired by the so-called coupling method that has been developed for the self-adjoint case by Henk de Snoo and his coauthors.

Iterative Solution for Systems of a Class of Abstract Operator Equations in Banach Spaces and Application

In this paper, by using the partial order method, the existence and uniqueness of a solution for systems of a class of abstract operator equations in Banach spaces are discussed. The result obtained in this paper improves and unifies many recent results. Two applications to the system of nonlinear differential equations and the systems of nonlinear differential equations in Banach spaces are given, and the unique solution and interactive sequences which converge the unique solution and the error estimation are obtained.

Regular approximation of singular Sturm–Liouville problems with eigenparameter dependent boundary conditions

In this paper we consider singular Sturm–Liouville problems with eigenparameter dependent boundary conditions and two singular endpoints. The spectrum of such problems can be approximated by those of the inherited restriction operators constructed. Via the abstract operator theory, the strongly resolvent convergence and norm resolvent convergence of a sequence of operators are obtained and it follows that the spectral inclusion of spectrum holds. Moreover, spectral exactness of spectrum holds for two special cases.

Exact Solutions to the Maxmin Problem max‖Ax‖ Subject to ‖Bx‖≤1

In this manuscript we provide an exact solution to the maxmin problem max ∥ A x ∥ subject to ∥ B x ∥ ≤ 1 , where A and B are real matrices. This problem comes from a remodeling of max ∥ A x ∥ subject to min ∥ B x ∥ , because the latter problem has no solution. Our mathematical method comes from the Abstract Operator Theory, whose strong machinery allows us to reduce the first problem to max ∥ C x ∥ subject to ∥ x ∥ ≤ 1 , which can be solved exactly by relying on supporting vectors. Finally, as appendices, we provide two applications of our solution: first, we construct a truly optimal minimum stored-energy Transcranian Magnetic Stimulation (TMS) coil, and second, we find an optimal geolocation involving statistical variables.

How Combinatory Logic Can Limit Computing Complexity

As computing capabilities are extending, the amount of source code to manage is inevitably becoming larger and more complex. No matter how hard we try, the bewildering complexity of the source code always ends up overwhelming its own creator, to the point of giving the appearance of chaos. As a solution to the cognitive complexity of source code, we are proposing to use the framework of Combinatory Logic to construct complex computational concepts that will provide a model of description of the code that is easy and intuitive to grasp. Combinatory Logic is already known as a model of computation but what we are proposing here is to use a logic of combinators and operators to reverse engineer more and more complex computational concept up from the source code. Through the two key notions of computational concept and abstract operator, we will show that this model offers a new, meaningful and simple way of expressing what the intricate code is about.

An exact solution method for Fredholm integro-differential equations

Introduction: Linear boundary value problems for Fredholm ordinary integro-differential equations are seldom consideredwith integral boundary conditions in the literature. In our case, integro-differential equations are subject to multipoint or nonlocalintegral boundary conditions. It should be noted that finding exact solutions even for multipoint problems or problems with nonlocalintegral boundary conditions with a differential equation is a difficult task. Purpose: Finding the uniqueness and existencecriterion of solutions for Fredholm ordinary integro-differential equations with multipoint or nonlocal integral boundary conditionsand obtaining exact solutions in closed form of such problems. Results: Within the class of abstract operator equations, for thespecial case of Fredholm integro-differential equations with multipoint or nonlocal integral boundary conditions, a criterion for theexistence and uniqueness of an exact solution is proved and the analytical representation of the solution is given. A direct methodanalytically solving such problems is proposed, in which all calculations are reproducible in any program of symbolic calculations.If the user sets the input parameters and the initial conditions of the problem, the computer codes check the conditions of existenceand uniqueness and of solution generate the analytical solution. The stages of the solution method are illustrated by twoexamples. The article uses computer algebra system Mathematica to demonstrate the results.

MATHEMATICAL AND LOGICAL MODEL OF AIRCRAFT TIMETABLES

The article analyses the methods of forming the aircraft flight schedule based on the classical theory of schedules as a theory of multi-stage systems. It is shown that the timetable is a system without interruptions, since each specific flight at a certain point in time is carried out by only one aircraft. In accordance with the theory of schedules, the optimal distribution of a discrete finite set of requirements serviced by deterministic systems with one or more devices is analysed under various assumptions about the nature of their maintenance. It is shown that the weakest assumption regarding the abstract operator, which translates many requirements into many agreed and executed plans, is the monotonic and unimodal behaviour of the corresponding functional of the generated plans. The possibilities of applying the theory of multi-stage systems to create the optimal schedule for medium or large airlines are investigated. The basic requirements for constructing a schedule are advanced. Mathematical models of the schedule are constructed taking into account the basic data of the current movement of aircraft in the area of ​​the airport or air hub. It has been established that if the base airports change their purpose and act as terminal arrival airports, the corresponding matrix elements are inversely symmetric, and with a rarefied spatial distribution of airports, the matrix can tend to diagonally dominant. A comparative analysis of scheduling algorithms is performed (based on queuing models, based on lists with the distribution of flights over time, etc.). The most suitable indicators of the effectiveness of the formation of the optimal schedule and system of priorities were selected and justified, taking into account the advantages of the arrival and departure times of passenger flights. An expression is derived for the resulting functional schedule efficiency, with which you can get quantitative comparative assessments of the quality of the schedule.

On Solvability of Third-Order Operator Differential Equation with Parabolic Principal Part in Weighted Space

Sufficient conditions are found for the correct and unique solvability of a class of third-order parabolic operator differential equations, whose principal parts have multiple characteristics, in a Sobolev-type space with exponential weight. The estimates for the norms of intermediate derivative operators are obtained and the relationship between these estimates and solvability conditions is established. Besides, the connection is found between the order of exponential weight and the lower bound for the spectrum of abstract operator appearing in the principal part of the equation.