A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes

We consider the following repulsive-productive chemotaxis model: find u ≥ 0, the cell density, and v ≥ 0, the chemical concentration, satisfying $$ \left\{ \begin{array}{l} \partial_t u - {\Delta} u - \nabla\cdot (u\nabla v)=0 \ \ \text{ in}\ {\Omega},\ t>0,\\ \partial_t v - {\Delta} v + v = u^p \ \ { in}\ {\Omega},\ t>0, \end{array} \right. $$ ∂ t u − Δ u − ∇ ⋅ ( u ∇ v ) = 0 in Ω , t > 0 , ∂ t v − Δ v + v = u p i n Ω , t > 0 , with p ∈ (1, 2), ${\Omega }\subseteq \mathbb {R}^{d}$ Ω ⊆ ℝ d a bounded domain (d = 1, 2, 3), endowed with non-flux boundary conditions. By using a regularization technique, we prove the existence of global in time weak solutions of (1) which is regular and unique for d = 1, 2. Moreover, we propose two fully discrete Finite Element (FE) nonlinear schemes, the first one defined in the variables (u,v) under structured meshes, and the second one by using the auxiliary variable σ = ∇v and defined in general meshes. We prove some unconditional properties for both schemes, such as mass-conservation, solvability, energy-stability and approximated positivity. Finally, we compare the behavior of these schemes with respect to the classical FE backward Euler scheme throughout several numerical simulations and give some conclusions.

Analysis of fully discrete, quasi non-conforming approximations of evolution equations and applications

In this paper, we consider fully discrete approximations of abstract evolution equations, by means of a quasi non-conforming spatial approximation and finite differences in time (Rothe–Galerkin method). The main result is the convergence of the discrete solutions to a weak solution of the continuous problem. Hence, the result can be interpreted either as a justification of the numerical method or as an alternative way of constructing weak solutions. We set the problem in the very general and abstract setting of pseudo-monotone operators, which allows for a unified treatment of several evolution problems. The examples — which fit into our setting and which motivated our research — are problems describing the motion of incompressible fluids, since the quasi non-conforming approximation allows to handle problems with prescribed divergence. Our abstract results for pseudo-monotone operators allow to show convergence just by verifying a few natural assumptions on the operator time-by-time and on the discretization spaces. Hence, applications and extensions to several other evolution problems can be easily performed. The results of some numerical experiments are reported in the final section.

Numerical approximation of control problems of non-monotone and non-coercive semilinear elliptic equations

We analyze the numerical approximation of a control problem governed by a non-monotone and non-coercive semilinear elliptic equation. The lack of monotonicity and coercivity is due to the presence of a convection term. First, we study the finite element approximation of the partial differential equation. While we can prove existence of a solution for the discrete equation when the discretization parameter is small enough, the uniqueness is an open problem for us if the nonlinearity is not globally Lipschitz. Nevertheless, we prove the existence and uniqueness of a sequence of solutions bounded in $$L^\infty (\varOmega )$$ L ∞ ( Ω ) and converging to the solution of the continuous problem. Error estimates for these solutions are obtained. Next, we discretize the control problem. Existence of discrete optimal controls is proved, as well as their convergence to solutions of the continuous problem. The analysis of error estimates is quite involved due to the possible non-uniqueness of the discrete state for a given control. To overcome this difficulty we define an appropriate discrete control-to-state mapping in a neighbourhood of a strict solution of the continuous control problem. This allows us to introduce a reduced functional and obtain first order optimality conditions as well as error estimates. Some numerical experiments are included to illustrate the theoretical results.

Implementasi Metode Promethee dalam Penentuan Penerima Bantuan Zakat pada Mahasiswa

During the payment of a single tuition fee (UKT) every semester, students are always faced with the problem of outstanding students but unable to pay tuition fees. Therefore, the university provides a solution to give zakat obtained from lecturers to outstanding and underprivileged students through the selection process. So far, the student selection process is still done manually, not using a system or program. So that the distribution of educational aid recipients (zakat) is considered not on target. This will certainly be a continuous problem of injustice, especially now that we have entered the digital era 4.0, all processes use a digital system. The provision of educational fund assistance in the form of zakat must be based on established rules, in this case the rules are in the form of established criteria, namely student IP, parental income, number of siblings, number of dependents of parents, semester, and others. The purpose of this study is to test whether the Promethee method is a method that can solve these problems. In addition, this research also forms a flow chart for selecting recipients of educational assistance using the Promethee method. The results of this study indicate that the problem of determining recipients of zakat assistance by students can be solved using the PROMETHEE method. Promethee (Preference Ranking Organization for Enrichment Evaluation), This method is appropriate for determining recipients of zakat assistance.

Numerical Solution of Fractional Elliptic Problems with Inhomogeneous Boundary Conditions

The numerical solution of fractional-order elliptic problems is investigated in bounded domains. According to real-life situations, we assumed inhomogeneous boundary terms, while the underlying equations contain the full-space fractional Laplacian operator. The basis of the convergence analysis for a lower-order boundary element approximation is the theory for the corresponding continuous problem. In particular, we need continuity results for Riesz potentials and the fractional-order extension of the theory for boundary integral equations with the Laplacian operator. Accordingly, the convergence is stated in fractional-order Sobolev norms. The results were confirmed in a numerical experiment.

Human-Wildlife Conflict around Belo-Bira Forest, Dawro Zone, Southwestern Ethiopia

Human-wildlife conflict (HWC) is a continuous problem in the world and has a significant impact on both human and wildlife populations. This study was conducted to investigate the HWC around Belo-Bira Forest, Dawro zone, southwestern Ethiopia. We collected data from October 2019 to March 2020 through semistructured questionnaires, focus group discussion, direct observation, and key informant interviews. Our results show that crop damage and livestock predation were common problems caused by Papio anubis, Cercopithecus aethiops, Crocuta crocuta, Canis aureus, and Potamochoerus larvatus. Human population growth, habitat disturbance, proximity to natural forest, and competition between wildlife and livestock are the identified causes of HWC. Moreover, the study identified guarding and fencing as dominant traditional methods used to reduce HWC in our study area. Therefore, local communities can minimize crop loss by using the most effective method in an area, and crops such as wheat, maize, and teff should not be grown near the forest edge.

Bacteriological profile of clinical isolates in cancer patients with febrile neutropenia in a tertiary care hospital in Kurnool, Andhra Pradesh

In cancer patients, infection is the most significant and continuous problem. This study was done to show the spectrum of bacteria and sites of isolation in febrile neutropenic cancer patients. A 1-year study of all isolates was conducted from various sites in our hospital. All the samples were processed, and isolates were identified as per CLSI guidelines. The commonest organism isolated was Escherichia coli among Gram negative organisms and Staphylococcus aureus among Gram positive organism. Out of 76 isolates 49 were Gram negative and 27 were Gram positive. The pattern of infectious agents has changed in neutropenic patients over time and this postulates the need of other studies to give the most up to date insight of the causative organism to the physician.

Discrete Dividend Payments in Continuous Time

We propose a model in which dividend payments occur at regular, deterministic intervals in an otherwise continuous model. This contrasts traditional models where either the payment of continuous dividends is controlled or the dynamics are given by discrete time processes. Moreover, between two dividend payments, the structure allows for other types of control; we consider the possibility of equity issuance at any point in time. The value is characterized as the fixed point of an optimal control problem with periodic initial and terminal conditions. We prove the regularity and uniqueness of the corresponding dynamic programming equation and the convergence of an efficient numerical algorithm that we use to study the problem. The model enables us to find the loss caused by infrequent dividend payments. We show that under realistic parameter values, this loss varies from around 1%–24% depending on the state of the system and that using the optimal policy from the continuous problem further increases the loss.

EXPERIMENTAL-THEORETICAL CALCULATION OF THE STRESS-DEFORMED STATE OF THE BAR ON THE ELASTIC BASIS

Any strip foundation, and sometimes a slab foundation can be consideredas a be a mon an elastic base. And if with calculation of a beam – the tape base problems practically do not a rise because loading on the tape base as a rule is evenly distributed, and means and the base be haves, a sabsolutelyrigid beam. Then when considering a section of the foundation with unevenlyapplied load, some problems may arise. Today there are many publications on studies of the use of beams with an elastic base in the field of construction and the application of the features of the method of calculating the stress-strain state in the field of design. As is known, from classical soil mechanics, when a load is applied to a flexible slab, its center gives a draft of 1.24-1.57 times greater than the edges. Note that this effect can be explained by the contour work of the base and its uneven stiffness in the central and peripheral zone of the slab foundation. It should be noted that today in most cases the method of BN Zhemochkin [6] is used as the basis for the analytical solution of the problem of the interaction of the beam with the elastic base, which combines an engineering approach and strict solutions of the theory of elasticity. According to research, the method is based on the replacement of the continuous problem of the interaction of the foundation beam with the soil base, discrete, with a limited number of calculated sections within the beam and approximation of the smooth reactive pressure curve stepped with a constant value within a single section. Such simplifications allow to calculate various engineering problems on interaction of beams and plates, including with difficult geometry with the set degree of accuracy, bypassing difficult differential and integral calculations.

An Extended Reselling Protocol for Existing Anti-Counterfeiting Schemes

Product counterfeiting is a continuous problem in industry. Recently, an anti-counterfeiting protocol to address this issue via radio-frequency identification (RFID) technology was proposed by researchers. Yet, the use case of reselling the same product has not been fully addressed which might cause serious problems for the exciting and proposed schemes and transactions. This paper proposes an extended RFID-based anti-counterfeiting protocol to address the use case of the original buyer reselling the same item to a second buyer. We will follow the proposed extended scheme with a formal security analysis to prove that the proposed protocol is secure and immune against most known security attacks.