Rational Expressions Research Articles

AN APPROACH TO THE STUDY OF FIXED POINT THEORY IN HILBERT SPACE

The purpose of this article is to extend Banach’s contraction principle through a new rational expression in the contractive condition to establish the existence and uniqueness of fixed point of a closed subset of Hilbert space to a self mapping. The result is extended to a pair of self mappings and positive integers powers of a pair mapping and further extended to a sequence of mappings in the space. The presented results extend and generalized various known comparable results from the current literature.

Weighted Linear Dynamic Logic

We introduce a weighted linear dynamic logic (weighted LDL for short) and show the expressive equivalence of its formulas to weighted rational expressions. This adds a new characterization for recognizable series to the fundamental Schützenberger theorem. Surprisingly, the equivalence does not require any restriction to our weighted LDL. Our results hold over arbitrary (resp. totally complete) semirings for finite (resp. infinite) words. As a consequence, the equivalence problem for weighted LDL formulas over fields is decidable in doubly exponential time. In contrast to classical logics, we show that our weighted LDL is expressively incomparable to weighted LTL for finite words. We determine a fragment of the weighted LTL such that series over finite and infinite words definable by LTL formulas in this fragment are definable also by weighted LDL formulas. This is an extended version of [17].

Fixed-Point Results for Generalized Rational Contractions in Graphical b-Metric Spaces with Applications

The aim of this paper is to define generalized rational contractions in the setting of graphical b -metric spaces and obtain some fixed-point theorems. Our results are significant generalizations and extensions of some well-known results in the existing theory. We also supply a nontrivial example to show the validity of the obtained theorems. As applications, we obtain some results on rational expressions in the background of graphical metric spaces.

Expansive Type Rational Contraction in Metric Space and Common Fixed Point Theorems

The field of expansive mappings in fixed-point theory is one of the most fascinating areas in mathematics. In this theory, contraction is one of the main tools used to prove a fixed point's existence and uniqueness. For all of the analyses, the fixed point theorem proposed by Banach's contraction theory is highly popular and widely used to prove that a solution to the operator equation Tx=x exists and is unique. Through the present article, we utilize rational expressions in metric spaces to deliver unique common stable (fixed) point results in expansive mapping. The main outcomes of numerous relevant innovations in the newest research are built upon them.

Berinde-Type Generalized \(\alpha\) - \(\beta\) - \(\psi\) Contractive Mappings in Partial Metric Spaces and Some Related Fixed Points

Aims/ Objectives: The objective of this paper is to introduce the notion of generalized \(\alpha\) - \(\beta\) - \(\psi\) contractive mappings involving rational expressions and establish existence and uniqueness of fixed points of Berinde type generalized \(\alpha\) - \(\beta\) - \(\psi\) contractive mappings in the context of partial metric spaces. Additionally, we provide an example in support of our results.

A Unified Wide-Speed Range Sensorless Control Method for Switched Reluctance Machines Based on Unsaturated Reluctance

A unified unsaturated-reluctance-based wide speed range sensorless control method for switched reluctance machines (SRMs) is proposed in this paper. Firstly, the sensitivity analysis of the estimated position to the possible reluctance calculation error is analyzed. This analysis reveals the feasible regions with low sensitivity and low risk of entering saturation. Then, the unsaturated reluctance in these feasible regions is obtained and modeled. A simple second-order rational expression is proposed to fit the highly nonlinear unsaturated reluctance curve. With this simple model, the rotor position can be analytically calculated only by solving a simple quadratic problem. Based on the above-presented analysis, a wide-speed range sensorless control is developed. The rotor position is universally estimated from the real-time reluctance value and the proposed analytical model. The high-frequency voltage injection and normal conduction phase are combined to calculate the phase reluctance over the wide-speed range. The concerns of calculating reluctance at the low-speed range are also discussed. A 5.1 kW four-phase 8/6 SRM is used to verify the proposed method. Various steady state and transient state experimental results prove the effectiveness of the proposed sensorless control method.

On sediment incipient motion of marine cohesive sediments with different bulk densities

This paper aims to methodically examine the incipient characteristics of natural marine fine sediment with particle size less than 0.012 mm for a variety range of bulk densities. Theoretical derivation and experimental data analysis are appropriately combined to explore the effect of bulk density on the inter-particle cohesive force and to deduce the incipient shear stress (ISS) of fine sediment. Under the same particle size condition, the achieved results indicate that the ISS of sediment intensifies with the growth of the bulk density. In addition, the larger the bulk density, the faster the increase rate, revealing a power exponential growth trend. The ISS of sediment also magnifies with the reduction of the particle size under the same bulk density condition; however, as the particle size decreases to 0.007 mm, the ISS of sediment would no longer vary. The influential factors on the cohesive force, including intermolecular gravitational force, film water pressure, and bulk density, are thoroughly analyzed, and a rational expression for the cohesive force is also proposed. The modified shields parameter represents the ratio between the sediment driving force and the stabilization force (e.g., gravitational and cohesive forces) and is still a function of the sediment Reynolds number. The modified shields curve still follows the shape of the original shields curve and satisfies both cohesive and non-cohesive sediment conditions but with differences in the form of shields parameter.

A transverse failure criterion for unidirectional composites based on the Puck failure surface theory

Puck criterion, a transverse failure criterion for composites, has more applications in engineering, but the empirical nature of its mathematical expression and the complexity of its parameters hinder its further development. In this work, a failure function is proposed based on the Puck hypothesis. According to the parameters of composites in special states, two modes of transverse tension and compression are distinguished, the pending coefficients in the failure function are derived, and then a transverse failure criterion for composites is formulated. The proposed criterion was evaluated experimentally in terms of envelope curves and off-axis strength using the existing data in the literature, and was compared with several other criteria. The results show that the proposed criterion is in good agreement with the experimental data, and its prediction accuracy ranks high among several criteria, demonstrating the rationality of the proposed criterion. Additionally, the effect of material parameters on the proposed criterion is analyzed and the results show that changes in transverse tensile and compressive strength can change the strengthening effect of transverse compression against in-plane shear, while changes in in-plane shear strength cannot change the strengthening effect. This work provides a correction method for the Puck criterion, which has a more rational mathematical expression with fewer parameters and can be used in the design of engineering composite structures, which has significant design reference value and theoretical significance.

Symbolic Treatment of Trigonometric Parametrizations: The General Unirational Case and Applications

AbstractIn this paper, we consider symbolic (hybrid trigonometric) parametrizations defined as tuples of real rational expressions involving circular and hyperbolic trigonometric functions as well as monomials, with the restriction that variables in each block of functions are different. We prove that the varieties parametrizable in this way are exactly the class of real unirational varieties of any dimension. In addition, we provide symbolic algorithms to implicitize and to convert a hybrid trigonometric parametrization into a unirational one, and vice versa. We illustrate by some examples the applicability of having these different types of parametrizations, namely, hybrid trigonometric and unirational.

Analytical Derivation of Scattering and Admittance Rational Functions From Coupling Matrix

The coupling matrix provides an immediate tool to describe a network, widely used in the context of microwave filters. While several techniques exist to obtain and manipulate the coupling matrix for a given response, the opposite is traditionally achieved by numerically evaluating the response of the network at each frequency of interest and fitting the response to obtain the rational expressions embedding poles and zeros. The present manuscript instead proposes an analytic way to retrieve directly the admittance and scattering functions, as ratios of polynomials, from the coupling matrix. Applications include commercial software packages and more robust microwave filter optimizations during design.

The impact of expression vector position on transgene transcription allows for rational expression vector design in a targeted integration system.

Site-specific integration (SSI) technology has emerged as an effective approach by the pharmaceutical industry for the development of recombinant Chinese hamster ovary (CHO) cell lines. While SSI systems have been demonstrated to be effective for the development of CHO cell lines, they can be limiting in terms of both transgene expression and in the case of multi-specifics, the ability to generate the correct product of interest. To maximize the performance of Pfizer's dual SSI expression system for expressing monoclonal and multi-specific antibodies, we used a novel approach to investigate the positional effect of transgenes within expression vectors by engineering nucleotide polymorphisms (NP)s to use as biomarkers to track the level of transcript output from each expression vector position. We observed differences in transcript level for two different transgenes across all four expression vector positions interrogated. We then applied these learnings to rationally design expression vectors for six different mAbs and a multi-specific antibody. We showed enhanced productivity and optimal product quality when compared to a conventional expression vector topology. The learnings gained here can potentially aid in the determination of optimal vector topologies for several IgG-like multi-specific formats.

“Feel My Rage”: Angry Feminist Claims and Affective Mobilization

In this article, I ask, “How do angry feminist claims get heard?” Angry feminist claims, I argue, inform, and mobilize by resonating with empathetic communities, legitimating feelings and experiences, and triggering energetic transfers among feminists and non-feminists. Through analysis of the 2018 protests of the nomination and confirmation of Brett Kavanaugh to the United States Supreme Court, I illustrate how angry feminist claims can be reclaimed as rational expressions of injustice, prompting divergent responses among differently situated audiences. Further, I demonstrate how anger as part of an affective appeal activates those attuned to hearing angry feminist claims as rational and legitimate, while simultaneously being challenged by intragroup intersectional differences.

Removing the Froissart Doublets in a Rational Interpolation Based on Loewner Matrix

In order to implement wide band frequency sweeping, the S-parameters can be fitted with an adaptive rational interpolation based on Loewner matrix. However, the errors in the sampling data may lead to Froissart doublets, which look like spikes in the curve. In this paper, a novel technique is proposed to remove these doublets. At first, the rational expression is converted into the sum of partial fractions by solving two generalized eigenvalue problems. After that, the partial fraction term with the smallest imaginary part of the pole and relatively large absolute value is considered to generate the doublets. Removing this term results in a smooth rational polynomial, which is validated by the example of a passive circuit simulated by finite element method(FEM).

Development and Validation of Learning Activity Sheets in Rational Expressions and Linear Equations and Inequalities

The purpose of this research study is to develop Learning Activity Sheets (LAS) in Rational Expressions and Linear Equations and Inequalities for the students. Data were collected via survey questionnaire from three sets of evaluators. The LAS was also administered from 100 students of New Society National High School to further scrutinize its validity. The results were interpreted and analysed using the rating scale and statistical tools including on-way ANOVA and mean.
 Based from the results of the study, the researcher concluded that: there were fourteen competencies included in the developed LAS which are the not mastered and least mastered competencies of the students. The competency that received the highest mean percentage on the competency test was LAS 17 (graphs and illustrates a linear function and its (a) domain; (b) range; (c) table of values; (d) intercepts; and (e) slope). On the other hand, the competency that received the lowest mean percentage on the competency test was LAS 12 (solves problems involving systems of linear inequalities in two variables). The evaluators found the developed LAS to be effective and useful in terms of objectives, concepts, skills, usability, appropriateness, and adequacy with an interpreted mean rating of very high extent. The researcher also concluded that there is no significant difference in the standard response of the evaluators which is composed of Grade 8 math teachers, master teachers, and LRMDS-trained teachers. Based on the mean percentage results of the administered LAS, there was also a considerable improvement in the students' learning.

Divisibility conditions on the order of the reductions of algebraic numbers

Let K K be a number field, and let G G be a finitely generated subgroup of K × K^\times . Without relying on the Generalized Riemann Hypothesis we prove an asymptotic formula for the number of primes p \mathfrak p of K K such that the order of ( G mod p ) (G\bmod \mathfrak p) is divisible by a fixed integer. We also provide a rational expression for the natural density of this set. Furthermore, we study the primes p \mathfrak p for which the order is k k -free, and those for which the order has a prescribed ℓ \ell -adic valuation for finitely many primes ℓ \ell . An additional condition on the Frobenius conjugacy class of p \mathfrak p may be considered. In order to establish these results, we prove an unconditional version of the Chebotarev density theorem for Kummer extensions of number fields.

Common fixed point results for a generalized ( ψ, φ )-rational contraction

In this paper, we obtain two common fixed point results for mappings satisfying the generalized (ψ,φ)-contractive type conditions given by a rational expression on a complete metric space. Our results generalize several well known theorems of the literature in the context of (ψ,φ)-rational contraction. In addition, there is an example for obtained results.

A New Look at the Fundamental Triangle Inequality

Summary We give a simple proof of the fundamental inequality of the triangle based on calculation of the cosine of an angle in one particular triangle formed from familiar centers. For the term which appears in the inequality we give a bound as a rational expression in terms of and . Then as an application we derive new refinements of Gerretsen’s and Kooi’s inequalities.

Linguistic Relativism and the Expression of Basic Theoretical Rationality in Inuktitut

This paper begins by stressing the importance of distinguishing between linguistic relativity, whose reality is hardly debatable, and linguistic relativism, which ultimately holds that language communities are locked within their own worldview, hence their own notions of truth. It then rejects linguistic relativism by asserting the existence of a universal core of theoretical rationality comprised at the very least of the logical principles of identity, noncontradiction, and excluded middle. It goes on to show how this theoretical rationality manifests itself in the lexicon of a language that differs greatly from English: Inuktitut spoken by Inuit of Nunavik (Arctic Quebec). The definitions provided by Taamusi Qumaq for three words relating to critical thought are translated for the first time. Other quotes give examples of theoretical rationality in actual usage. Finally, the paper asks why logic as such is accorded little value in the culture Inuktitut expresses. The suggested answer follows Jack Goody, who holds that a long written tradition is required for the rules of formal logic to take hold in language practices. Writing is not just a transcription of the spoken word; it is an intellectual technology that impacts the way speakers use their language.

A novel numerical method for predicting the hydration heat of concrete based on thermodynamic model and finite element analysis

In this study, a rational theoretical expression and effective numerical realization of the hydration temperature evolution of concrete are presented. The proposed novel numerical method is based on the Fourier's law for heat flux, the heat source function which is obtained from the dissolution of cement clinker by the modified Parrot and Killoh model, and also takes into account the Arrhenius equation. Experimental temperature measurements performed on three different specimens under semi-adiabatic and adiabatic conditions are used to validate the proposed model. The results show that the measured semi-adiabatic and adiabatic temperatures of the SCM-blended concrete mixtures are in general agreement with the simulation results. The method proposed in this study can also predict the temperature field of mass concrete, providing guidance for practical engineering.

Thermodynamically consistent stochastic models for active transmembrane transport processes.

Simulating the full transport cycle of an active transporter driven an ionic electrochemical transmembrane gradient with atomistic detail has been challenging because full cycle completions occur on typical time scales ranging from milliseconds to seconds, out of reach of typical molecular dynamic (MD) simulations. Instead, multiscaling approaches have been developed that break the cycle into elementary steps for which kinetic and equilibrium parameters can be obtained from MD. These parameters are combined in a stochastic kinetic model whose master equation is solved under varying external conditions such as ion concentrations and membrane potential. We developed two improvements for this well-known approach: (1) We introduce the multibind algorithm to derive thermodynamically consistent state free energies and rates from input free energy differences and rates; without such a step, a kinetic model is not guaranteed to obey the laws of thermodynamics and may produce nonsensical results. We also show how the resulting model can be used for parameter inference of microscopic parameters from macroscopic experimental measurements. (2) As an alternative to the numerical solution of the steady state problem, one can exactly solve it using Hill's diagrammatic approach. Our Kinetic Diagram Analysis (KDA) implementation of Hill's method yields symbolic rational expressions for arbitrary kinetic graphs that can be analytically manipulated and directly evaluated. We demonstrate the kinetic graph multiscale approach for sodium/proton antiporters.