Method to solve integral equations of the first kind with an approximate input

Techniques are proposed for solving integral equations of the first kind with an input known not precisely. The requirement that the solution sought for includes a given number of maxima and minima is imposed. It is shown that when the deviation of the approximate input from the true one is sufficiently small and some additional conditions are fulfilled the method leads to an approximate solution that is necessarily close to the true solution. No regularization is required in the present approach. Requirements on features of the solution at integration limits are also imposed. The problem is treated with the help of an ansatz proposed for the derivative of the solution. The ansatz is the most general one compatible with the above mentioned requirements. The techniques are tested with exactly solvable examples. Inversions of the Lorentz, Stieltjes and Laplace integral transforms are performed, and very satisfactory results are obtained. The method is useful, in particular, for the calculation of quantum-mechanical reaction amplitudes and inclusive spectra of perturbation-induced reactions in the framework of the integral transform approach.Comment: 28 pages, 1 figure; the presentation is somewhat improved; to be published in Phys. Rev.

P Systems with Minimal Left and Right Insertion and Deletion

In this article we investigate the operations of insertion and deletion performed at the ends of a string. We show that using these operations in a P systems framework (which corresponds to using specific variants of graph control), computational completeness can even be achieved with the operations of left and right insertion and deletion of only one symbol

On insertion-deletion systems over relational words

We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation between their labels. We define the operations of insertion and deletion on relational words generalizing corresponding operations on strings. We prove that the transitive and reflexive closure of these operations has a decidable membership problem for the case of short insertion-deletion rules (of size two/three and three/two). At the same time, we show that in the general case such systems can produce a coding of any recursively enumerable language leading to undecidabilty of reachability questions.Comment: 24 pages, 8 figure

Polynomial reconstruction of electric charge distribution on the conductive plate caused by external electric field

The paper proposes an original method of calculating the charge distribution on the surface of the conductive plate introduced into the external electrostatic field. The authors managed to obtain the polynomials which allow to solve the integral equation that establishes the relationship between charge distribution of the conductive plate and the potential distribution of the external field and the potential on the surface of the plate. The proposed algorithms solutions are valid in the presence of axial symmetry of the field and the plate. Examples of calculation of conductor charge distribution in the presence of external field by using a polynomial expansion have been presented. The comparisons of results calculated by the polynomial method and by known analytical solutions have been given

Spiking neural P systems: matrix representation and formal verification

YesStructural and behavioural properties of models are very important in development of complex systems and applications. In this paper, we investigate such properties for some classes of SN P systems. First, a class of SN P systems associated to a set of routing problems are investigated through their matrix representation. This allows to make certain connections amongst some of these problems. Secondly, the behavioural properties of these SN P systems are formally verified through a natural and direct mapping of these models into kP systems which are equipped with adequate formal verification methods and tools. Some examples are used to prove the effectiveness of the verification approach.EPSRC research grant EP/R043787/1; DOST-ERDT research grants; Semirara Mining Corp; UPD-OVCRD

Design and baseline characteristics of the finerenone in reducing cardiovascular mortality and morbidity in diabetic kidney disease trial

Background: Among people with diabetes, those with kidney disease have exceptionally high rates of cardiovascular (CV) morbidity and mortality and progression of their underlying kidney disease. Finerenone is a novel, nonsteroidal, selective mineralocorticoid receptor antagonist that has shown to reduce albuminuria in type 2 diabetes (T2D) patients with chronic kidney disease (CKD) while revealing only a low risk of hyperkalemia. However, the effect of finerenone on CV and renal outcomes has not yet been investigated in long-term trials. Patients and Methods: The Finerenone in Reducing CV Mortality and Morbidity in Diabetic Kidney Disease (FIGARO-DKD) trial aims to assess the efficacy and safety of finerenone compared to placebo at reducing clinically important CV and renal outcomes in T2D patients with CKD. FIGARO-DKD is a randomized, double-blind, placebo-controlled, parallel-group, event-driven trial running in 47 countries with an expected duration of approximately 6 years. FIGARO-DKD randomized 7,437 patients with an estimated glomerular filtration rate >= 25 mL/min/1.73 m(2) and albuminuria (urinary albumin-to-creatinine ratio >= 30 to <= 5,000 mg/g). The study has at least 90% power to detect a 20% reduction in the risk of the primary outcome (overall two-sided significance level alpha = 0.05), the composite of time to first occurrence of CV death, nonfatal myocardial infarction, nonfatal stroke, or hospitalization for heart failure. Conclusions: FIGARO-DKD will determine whether an optimally treated cohort of T2D patients with CKD at high risk of CV and renal events will experience cardiorenal benefits with the addition of finerenone to their treatment regimen. Trial Registration: EudraCT number: 2015-000950-39; ClinicalTrials.gov identifier: NCT02545049