Monotonicity Techniques Research Articles

A Hybrid Energy-Efficient, Area-Efficient, Low-Complexity Switching Scheme in SAR ADC for Biosensor Applications.

A hybrid energy-efficient, area-efficient, low-complexity switching scheme in SAR ADC for biosensor applications is proposed. This scheme is a combination of the monotonic technique, the MSB capacitor-splitting technique, and a new switching method. The MSB capacitor-splitting technique, as well as the reference voltage Vaq allow for more options for reference voltage conversion, resulting in higher area savings and higher energy efficiency. In a capacitor array, the circuit performs unilateral switching during all comparisons except for the second and last two comparisons, reducing the difficulty in designing the drive circuit. The proposed switching scheme saves 98.4% of the switching energy and reduces the number of unit capacitors by 87.5% compared to a conventional scheme. Furthermore, the SAR ADC employs low-noise and low-power dynamic comparators utilizing multi-clock control, low-sampling error-sampling switches based on the bootstrap technique, and dynamic SAR logic. The simulation results demonstrated that the proposed SAR ADC achieves 61.51 dB SNDR, 79.21 dB SFDR and consumes 0.278 μW of power in a 180 nm process with a 1 V power supply, a full swing input signal frequency of 23.33 kHz, and a sampling rate of 100 kS/s.

Ground State Solutions of Fractional Choquard Problems with Critical Growth

In this article, we investigate a class of fractional Choquard equation with critical Sobolev exponent. By exploiting a monotonicity technique and global compactness lemma, the existence of ground state solutions for this equation is obtained. In addition, we demonstrate the existence of ground state solutions for the corresponding limit problem.

Solvability of nonlinear diffusion models with flux at the boundary driven by nonmonotone local and memory interactions

We investigate local and global solvability for nonlinear diffusion models with boundary flux driven by competing local and memory interactions. New local existence and comparison theories are developed for such models which are not amenable to a-priori arguments for nonnegative solutions, as well as not permitting standard monotonicity techniques of analysis. A transformation used to address nonnegativity subsequently results in classical solutions for strictly positive initial states. An alternating construction introduced to obtain solutions via monotone limits from above and below is somewhat reminiscent of the method of upper and lower solutions. Subsolution/supersolution comparison results that follow are applied to analyze boundedness, positivity, and blow up in finite time of solutions for power law cases of localized absorption and memory driven dissipation at the boundary. This connects the present work with our previous analyses of models having memory driven absorption at the boundary, shown to exactly parallel known results in cases of localized absorption, and begins to reveal comparative strengths of each.

Positive weak solutions for heterogeneous elliptic logistic BVPs with glued Dirichlet-Neumann mixed boundary conditions

<abstract><p>This article concerns the existence of positive weak solutions of a heterogeneous elliptic boundary value problem of logistic type in a very general annulus. The novelty of this work lies in considering non-classical mixed glued boundary conditions. Namely, Dirichlet boundary conditions on a component of the boundary, and glued Dirichlet-Neumann boundary conditions on the other component of the boundary. In this paper we perform a complete analysis of the existence of positive weak solutions of the problem, giving a necessary condition on the $ \lambda $ parameter for the existence of them, and a sufficient condition for the existence of them, depending on the $ \lambda $-parameter, the spatial dimension $ N \geq 2 $ and the exponent $ q > 1 $ of the reaction term. The main technical tools used to carry out the mathematical analysis of this work are variational and monotonicity techniques. The results obtained in this paper are pioners in the field, because up the knowledge of the autor, this is the first time where this kind of logistic problems have been analyzed.</p></abstract>

Assessment of the usability conditions of Sb2O3–PbO–B2O3 glasses for shielding purposes in some medical radioisotope and a wide gamma-ray energy spectrum

Abstract We report some fundamental gamma-ray shielding properties and individual transmission factors (TFs) of five distinct glass samples with a nominal composition of xSb2O3·(40 − x)PbO·60B2O3·0.5CuO and (where; 0 ≤ x ≤ 40 mol%). Phy-X/PSD and MCNPX (version 2.7.0) Monte Carlo code are utilized to determine several critical parameters, such as cross-sections, attenuation coefficients, half and tenth value layers, build-up factors, and TFs. A general transmission setup is designed using basic requirements. Accordingly, TFs are evaluated for several medical radioisotopes. Next, the gamma-ray shielding parameters and TFs are assessed together in terms of providing the validity of the findings. Our results showed that there is a positive contribution of increasing Sb2O3 amount in the glass matrix owing its direct effect to the density increment as well. This positive effect on gamma-ray shielding properties is also observed for decreasing mean free path values from S1 to S5 samples. The exposure build-up factor (EBF) and energy absorption build-up factor (EABF) values, increasing the quantity of Sb2O3 supplementation, resulted in a general reduction in EBF and EABF values (i.e., from 0.5 to 40 mfp). When the quantity of Sb2O3 rises from S1 to S5, the collision rate of incoming gamma rays in glass samples increases significantly. The TF figures reveal that S5 showed the least transmission behavior across all the above-mentioned studied glass thicknesses. It can be concluded that increasing the Sb2O3 additive is a beneficial and monotonic technique, when the gamma-ray shielding qualities or TF values must be further enhanced.

New Constructions of Obviously Strategyproof Mechanisms

Catering to the incentives of people with limited rationality is a challenging research direction that requires novel paradigms to design mechanisms. Obviously strategy-proof (OSP) mechanisms have recently emerged as the concept of interest to this research agenda. However, the majority of the literature in the area has either highlighted the shortcomings of OSP or focused on the “right” definition rather than on the construction of these mechanisms. Here, we give the first set of tight results on the approximation guarantee of OSP mechanisms for scheduling related machines and a characterization of set system instances for which OSP mechanisms that return optimal solutions exist. By extending the well-known cycle monotonicity technique, we are able to concentrate on the algorithmic component of OSP mechanisms and provide some novel paradigms for their design, when private types belong to a set with few values. In essence, we prove that OSP encompasses careful interleaving of ascending and descending auctions. Funding: Diodato Ferraioli was partially supported by GNCS-INdAM, and by the Italian MIUR [PRIN 2017 Project ALGADIMAR] (Algorithms, Games, and Digital Markets). Carmine Ventre was partially supported by the UKRI Trustworthy Autonomous Systems Hub [EP/V00784X/1].

Estafet Writing Method to Improve Arabic Writing Skills Outcomes: Experimental Study on Indonesian Middle School Students

One of the language skills that require a process of practicing, learning, and proper techniques for teaching students in writing. By intensive practicing and studying, students become skillful faster. It seems difficult for students to compile their writing without making careful planning before writing. Many students cannot express their opinion because the teacher does not teach them properly. Teaching writing with monotone techniques inhibits students to get the ideas provided by the teacher during the writing learning process. This research focused on the methods used by the teacher in Maharah Kitabah (writing skills), which was at relay writing method (chain writing). The research method used was experimental, that data was collected by observation and test. Then, the data were analyzed by using the N-Gain. From the results of the N-Gain test, the average score of the pre-test and post-test scores has increased by a percentage of 59%. While the average score obtained from the acquisition of the N-gain value is 0.72, therefore, the category was high. This result proves that the estafet writing method can improve Arabic writing skills outcomes.

Convergence on Population Dynamics and High-Dimensional Haddock Conjecture

One fundamental step towards grasping the global dynamic structure of a population system involves characterizing the convergence behavior (specifically, how to characterize the convergence behavior). This paper focuses on the neutral functional differential equations arising from population dynamics. With the help of monotonicity techniques and functional methods, we analyze the subtle relations of both the ω-limited set and special point. Meanwhile, we prove that every bounded solution converges to a constant vector, as t tends to positive infinity. Our results correlate with the findings from earlier publications, and our proof yields an improved Haddock conjecture.

Traveling Waves Solutions for Delayed Temporally Discrete Non-Local Reaction-Diffusion Equation

This paper deals with the existence of traveling wave solutions to a delayed temporally discrete non-local reaction diffusion equation model, which has been derived recently for a single species with age structure. When the birth function satisfies monotonic condition, we obtained the traveling wavefront by using upper and lower solution methods together with monotonic iteration techniques. Otherwise, without the monotonicity assumption for birth function, we constructed two auxiliary equations. By means of the traveling wavefronts of the auxiliary equations, using the Schauder’ fixed point theorem, we proved the existence of a traveling wave solution to the equation under consideration with speed c>c*, where c*>0 is some constant. We found that the delayed temporally discrete non-local reaction diffusion equation possesses the dynamical consistency with its time continuous counterpart at least in the sense of the existence of traveling wave solutions.

Qualitative results for finite system of R-L fractional differential equations with initial time difference

Qualitative results such as existence and uniqueness of finite system of Riemann-Liouville (R-L) fractional differential equations with initial time difference are obtained. Monotone technique coupled with method of lower and upper solutions is developed to obtain existence and uniqueness of solutions of finite system of R-L fractional differential equations with initial time difference.

Asymptotic behavior of solutions for time-delayed nonlocal dispersion equations with Dirichlet boundary

This paper is concerned with the asymptotic behavior of the solutions for Nicholson's blowflies equation with nonlocal dispersion subjected to Dirichlet boundary condition. We first prove the existence and uniqueness of the solution for the initial boundary value problem and its non-trivial steady state. Then we give a threshold result on global stability of equilibria: when , the solution time-exponentially converges to the constant equilibrium 0 for any large initial data; when , the solution time-asymptotically converges to its positive steady-state for any large initial data, once , where D>0 is the diffusion coefficient, is the death rate, p>0 is the birth rate and is the principal eigenvalue for the nonlocal characteristic equation. The adopted approach is the energy method and the monotonic technique.

Solving the Nonlinear Monotone Equations by Using a New Line Search Technique

In this work a new technique of line search is proposed to solve the nonlinear monotone equations. For this purpose we combine a modified line search rule with monotone technique. The new proposed algorithm can decrease the CPU time, the number of iterations and the functions evaluations and can increase the efficiency of the approach. The global convergence result of the recommended procedures is established under some standard conditions. Preliminary numerical results indicate that the proposed algorithm are interesting and remarkably promising.

Qualitative Properties of Solutions of Finite System of Differential Equations Involving R-L Sequential Fractional Derivative

In this paper, qualitative properties such as existence-uniqueness of solutions of finite system of differential equations involving R-L sequential fractional derivative with initial conditions have been studied. Lower and upper solutions are defined for the problem under investigation. Comparison results are used to develop monotone technique for finite system of differential equations involving R-L sequential fractional derivative with initial conditions when the functions on the right hand side are mixed quasi-monotone. Two convergent monotone sequences are obtained by introducing monotone operator. Lipschitz condition is the key part of the study. Minimal and maximal solutions are obtained by using developed technique. Existence and uniqueness of solutions of finite system of differential equations involving R-L sequential fractional derivative is also proved as an application of the technique.

Hybrid Compound Function/Subinterval Perturbation Method for Kinematic Analysis of a Dual-Crane System With Large Bounded Uncertainty

Abstract By introducing the subinterval perturbation method (SIPM), a hybrid compound function/subinterval perturbation method (HCFSPM) is presented for a dual-crane system (DCS) with large interval variables. The HCFSPM employs the SIPM to decompose a large interval variable into several subinterval variables with small uncertain levels. The interval kinematic compound function vectors and their inverses are approximated by the first-order Taylor and Neumann series, respectively. Based on the monotonic technique, the bounds of original luffing angle vectors are derived. Compared with the first-order compound function/interval perturbation method and the Monte Carlo method, numerical examples verify the effectiveness of the HCFSPM at conducting uncertain kinematic analysis of the DCS, especially when it comes to large uncertain levels.

Principal eigenvalues of elliptic BVPs with glued Dirichlet-Robin mixed boundary conditions. Large potentials on the boundary conditions

In this paper we perform a complete study about the existence, uniqueness and simplicity of the principal eigenvalue of a class of elliptic eigenvalue problems with glued Dirichlet-Robin boundary conditions on a component of the boundary of the domain and Dirichlet boundary conditions on the other component of the boundary. Moreover, this principal eigenvalue and its normalized principal eigenfunction are approached in R×H1(Ω) by principal eigen-pairs of boundary eigenvalue problems with classical mixed boundary conditions. In some sense, the glued mixed boundary conditions analyzed in this work may be regarded as classical mixed boundary conditions with large potentials in the Robin boundary condition. The principal eigenvalues analyzed in this paper, play a crucial role in analyzing the existence, uniqueness and asymptotic behavior of the positive solutions of certain kinds of semilinear elliptic boundary value problems with nonlinear boundary conditions and spatial heterogeneities. The main technical tools used to carry out the mathematical analysis of this work are variational and monotonicity techniques. The results in [2], [3] and [4] play a crucial role to obtain some of the results of this work.

Convergence in a system of critical neutral functional differential equations

In this study, we investigate the dynamic behavior on a system of neutral functional differential equations in critical case. Combining monotonicity techniques and functional methods, we develop the delicate monotonicity with the addressed system and show the convergence for every pre-compact solution with some initial condition, which improves and complements some existing ones.

Capacity Solution to a Nonlinear Elliptic Coupled System in Orlicz–Sobolev Spaces

We analyze the existence of a capacity solution to the following nonlinear elliptic coupled system, whose unknowns are the temperature inside a semiconductor material, u, and the electric potential, $$\varphi $$, $$\begin{aligned} \left\{ \begin{array}{ll} -Au= \rho (u)|\nabla \varphi |^2 &{}\quad \mathrm{in}\ \Omega , \\ \mathop {\mathrm{div}}\nolimits (\rho (u)\nabla \varphi ) =0&{}\quad \mathrm{in}\ \Omega , \\ \varphi =\varphi _0 &{}\quad \hbox {on } \partial \Omega , \\ u=0&{}\quad \mathrm{on}\, {\partial \Omega }, \end{array} \right. \end{aligned}$$where $$\Omega \subset {\mathbb {R}}^d$$, $$d\ge 2$$ and $$\displaystyle Au=-\mathop {\mathrm{div}}\nolimits a(x,u,\nabla u)$$ is a Leray–Lions operator defined on $$W_0^{1}L_M(\Omega )$$, M is a N-function which does not have to satisfy a $$\Delta _2$$ condition. Therefore, we work with generalized Orlicz–Sobolev spaces which are not necessarily reflexive. The function $$\varphi _0$$ is given. The proof combines truncation methods, monotonicity techniques and regularizing methods in Orlicz spaces. We introduce a sequence of approximate problems which converges (up to a subsequence) in a certain sense to a capacity solution in the context of non-reflexive Orlicz–Sobolev spaces.

Successive iteration technique for singular nonlinear system with four-point boundary conditions

In this paper, the existence of at least one positive solution of the system of singular differential equations with four-point coupled boundary conditions is discussed. A constructive monotonic iterative technique on the equivalent completely continuous nonlinear operator is used to establish the result. This method produces an approximate solution in the form of series which is very helpful in developing a numerical scheme for the positive solution of the system. It is demonstrated through the examples.

A modified Schr\xf6dinger-type identity: uniqueness of solutions for singular boundary value problem for the Schr\xf6dinger equation

This paper is devoted to modifying the Schrödinger-type identity related to singular boundary value problem in (Zhang et al. in Bound. Value Probl. 2018:135, 2018). We also present some mathematical consequences of the method, including a stability result. The main technical tools used to develop the mathematical analysis are local and global bifurcation, monotonicity techniques, fixed point theory in b-metric spaces in (Liu et al. in Bull. Aust. Math. Soc. 94(1):121–130, 2016) and the maximum principle approach with respect to the Schrödinger operator in (Fan et al. in Math. Appl. 31(1):42–48, 2018). As an application, the uniqueness of solutions for singular boundary value problem for the Schrödinger equation is proved.

Traveling waves solutions for partial neutral differential equations

Using monotonicity techniques and the Schauder fixed point theorem, we study the existence of traveling waves for neutral partial differential equations. In the last section, we illustrate our results on the neutral versions of the KPP-Fisher and the Kobayashi equations.