Rational Expressions Research Articles

Combinatorial metabolic engineering and tolerance evolving of Escherichia coli for high production of 2′-fucosyllactose

2′-Fucosyllactose (2′-FL) is an important functional ingredient of advanced infant formula. Here, Escherichia coli MG1655 was engineered for achieving high 2′-FL production. The expressions of 2′-FL synthesis pathway genes were finely regulated with single or multi copies according to rate-limiting enzyme diagnosis. On this basic, the branch pathway genes were deleted, and the overexpression of the 2′-FL efflux protein SetA and the fructose-1,6-bisphosphatase GlpX were tuned. The resulting strain produced 46.06 ± 1.28 g/L 2′-FL in a 5-L fermenter. Furtherly, adaptive laboratory evolution was conducted. A rpoC gene mutation was obtained which could improve the cell tolerance and the 2′-FL production up to 61.06 ± 1.93 g/L, with the highest productivity of 1.70 g/L/h among E. coli strains by now. Taken together, this work provides a combinatorial strategy to improve 2′-FL accumulation including rational fine-tuning pathway genes expressions and irrational adaptive laboratory evolution. This study should be helpful for constructing high level 2′-FL producers.

Fixed Point Results via Real-Valued Function Satisfying Integral Type Rational Contraction

In this article, we mainly discuss the existence and uniqueness of fixed point satisfying integral type contractions in complete metric spaces via rational expression using real-valued functions. We improve and unify many widely known results from the literature. Among these, the work of Rakotch (1962), Branciari (2002), and Liu et al. (2013) is extended. Finally, we conclude with an example presented graphically in favour of our work.

Support towards emergency event processing via fine-grained analysis on users' expressions

PurposeWith the rapid development of social media, the occurrence and evolution of emergency events are often accompanied by massive users' expressions. The fine-grained analysis on users' expressions can provide accurate and reliable information for event processing. Hence, 2,003,814 expressions on a major malignant emergency event were mined from multiple dimensions in this paper.Design/methodology/approachThis paper conducted finer-grained analysis on users' online expressions in an emergency event. Specifically, the authors firstly selected a major emergency event as the research object and collected the event-related user expressions that lasted nearly two years to describe the dynamic evolution trend of the event. Then, users' expression preferences were identified by detecting anomic expressions, classifying sentiment tendencies and extracting topics in expressions. Finally, the authors measured the explicit and implicit impacts of different expression preferences and obtained relations between the differential expression preferences.FindingsExperimental results showed that users have both short- and long-term attention to emergency events. Their enthusiasm for discussing the event will be quickly dispelled and easily aroused. Meanwhile, most users prefer to make rational and normative expressions of events, and the expression topics are diversified. In addition, compared with anomic negative expressions, anomic expressions in positive sentiments are more common. In conclusion, the integration of multi-dimensional analysis results of users' expression preferences (including discussion heat, preference impacts and preference relations) is an effective means to support emergency event processing.Originality/valueTo the best of the authors' knowledge, it is the first research to conduct in-depth and fine-grained analysis of user expression in emergencies, so as to get in-detail and multi-dimensional characteristics of users' online expressions for supporting event processing.

Chatterjea type theorems for complex valued extended $ b $-metric spaces with applications

<abstract><p>In this article, we establish common $ \alpha $ -fuzzy fixed point theorems for Chatterjea type contractions involving rational expression in complex valued extended $ b $-metric space. Our results generalize and extend some familiar results in the literature. Some common fixed point results for multivalued and single valued mappings are derived for complex valued extended $ b $-metric space, complex valued $ b $-metric space and complex valued metric space as consequences of our leading results. As an application, we investigate the solution of Fredholm integral inclusion.</p></abstract>

Common fixed point theorems on complex valued extended $ b $-metric spaces for rational contractions with application

<abstract><p>The purpose of this article is to establish common fixed point results on complex valued extended $ b $-metric spaces for the mappings satisfying rational expressions on a closed ball. Our investigations generalize some well-known results of literature. Furthermore, we supply a significant example to show the authenticity of established results. As application, we solve Urysohn integral equations by our main results.</p></abstract>

Chebyshev Approximation of Multivariable Functions by a Constrained Rational Expression

Chebyshev Approximation of Multivariable Functions by a Constrained Rational Expression

On generalized Suzuki-Proinov type (α,Z*E)−contractions in modular b−metric spaces

This paper?s objective is to put forward anewkind of E?type contraction, which includes rational expression, by considering Proinov type functions and CG?simulation functions. This type of contraction is termed as a Suzuki-Proinov type generalized (?,Z* E)?contraction mapping. Further, some common fixed point theorems using these new mappings, which are triangular ??admissible pairs, are demonstrated in the setting of modular b?metric space. Besides, the given example indicates the applicability and validity of the outcomes of this study.

Responses of SDOF Structures With SPIS-<b>Ⅱ</b> Dampers Under Random Seismic Excitation

A closed-form solution of response of SDOF structure with SPIS-II damper subjected to seismic excitation modeled by Clough-Pezien spectrum is proposed, and the shock absorption performance and influencing factors of that system are studied based on the proposed method. Firstly, the equation of motion of SPIS-II damper is established, and the unified expression of the structural response frequency domain solution such as structural displacement and inertial output force are obtained. Secondly, based on the rational expression decomposition and residue theorem, quadratic quadrature equations of frequency response eigenvalue function and Clough-Pezien spectrum are obtained respectively, and then quadratic quadrature equations of structural response power spectrum are induced. Thirdly, concise closed-form solutions of the 0 ~ 2 order spectral moments of the structural response are acquired. The proposed method and the virtual excitation method are used to analyze a case respectively, which verifies the correctness of the proposed method. Finally, the proposed method is used to analyze the influence of the parameters of inertia capacity on the seismic performance of the structure. The research shows that the response solution obtained by the method in this paper is a closed-form solution, which is better than the virtual excitation method in terms of computational efficiency and computational accuracy; when <i>μ</i>_<i>ω</i>unchanged, the damping performance is enhanced with the increasing of <i>μ</i>_<i>m</i>and <i>μ</i>_<i>ξ</i>; when <i>μ</i>_<i>ω</i>=1, the damping performance is improved to the greatest.

A Haskalah story: Kant and Maimon on rational faith

In 1789 Salomon Maimon sent Kant, via Markus Herz, the manuscript of his Essay on Transcendental Philosophy (Kant, 1999, pp. 291-294). A surprised Kant replied to Herz: “None of my critics understood me as well as Herr Maimon does” (Kant, 1999, pp. 311-315). Kant’s praise of Maimon makes him a singular figure in the Haskalah, the Jewish Enlightenment. But while the theoretical aspect of Maimon’s criticism of Kant has received increasing attention in recent years, its practical implications remain under-examined. In what follows, I use the notion of rational faith for the purposes of a tentative reconstruction of Maimon’s reading of Kant’s transcendental philosophy that brings together theoretical and practical aspects of the thought of both philosophers. Kant and Maimon shared a project of devising a form of faith that would express rational rather than religious-based morality. Kant argued for a rational moral freedom that is vouched by an infinite intellect that cannot be attributed to humans but more appropriately to God. For Maimon, the answers to the questions What can I know? and What should I do? involve a cognitive and affective process of striving to expand our finite consciousness. This process is the rational expression of God in us.

Upper Bounds on Mixing Time of Finite Markov Chains

We provide a general framework for computing upper bounds on mixing times of finite Markov chains when its minimal ideal is left zero. Our analysis is based on combining results by Brown and Diaconis with our previous work on stationary distributions of finite Markov chains. Stationary distributions can be computed from the Karnofsky--Rhodes and McCammond expansion of the right Cayley graph of the finite semigroup underlying the Markov chain. Using loop graphs, which are planar graphs consisting of a straight line with attached loops, there are rational expressions for the stationary distribution in the probabilities. From these we obtain bounds on the mixing time. In addition, we provide a new Markov chain on linear extension of a poset with $n$ vertices, inspired by but different from the promotion Markov chain of Ayyer, Klee and the last author. The mixing time of this Markov chain is $O(n \log n)$.

An Adaptive Rational Fitting Technique of Sommerfeld Integrals for the Efficient MoM Analysis of Planar Structures

The integral equation method is one of the most successful computational models for microwave devices or integrated circuits in planar layered media. However, the efficient and accurate evaluation of the associated Green’s function consisting of Sommerfeld integrals (SIs) is still a remaining challenge. To mitigate this difficulty, this work proposes a spatial domain rational function fitting technique (RFFT) for SIs so that the approximation accuracy is controllable. In conjunction with an adaptive sampling strategy, the proposed RFFT minimizes the orders of rational functions, and the resultant SI evaluation efficiency is optimized. In addition, we investigate the semi-analytical singularity treatment for the rational expression of SIs in method of moment (MoM) implementation. Extensive simulation of representative planar devices validates the correctness of the proposed method and demonstrates its superior performance over conventional SI approximation methods.

Development of a new method for modeling a physical system in a rational expression

The presented paper shows a new method for modeling of a physical system in a rational expression. The method is based on a hybrid combination of the conventional least square method (LSM) and a robust recursive procedure. In the first step of the method, a sampling function is employed to establish a system of linear equations. Then, the QR decomposition method and a very fast iterative technique are simultaneously used to determine the unknown parameters. Also, it is shown that by regarding a scalar gain parameter, the stability of the final model can be controlled. To verify the performance of the presented method, several theoretical and practical examples are examined and the obtained results are compared with the simulation and measurement data.

The dyadic care experiences of elderly individuals with disabilities and caregivers in the home setting from the perspective of family resilience: A qualitative study.

BackgroundChina is one of the most rapidly aging countries in Asia, and nearly 90% of elderly individuals with disabilities choose to receive traditional, family-based, long-term care. A majority of family caregivers have insufficient care capacity and experience physical and emotional distress, which in turn affects the elderly.ObjectiveTo describe the dyadic care experiences of elderly individuals with disabilities and their caregivers from the perspective of family resilience.MethodsA phenomenological research method was used. Semi-structured, in-depth, face-to-face interviews with 9 dyads of elderly people with disabilities and their families were conducted from August 2020 to February 2021. The Colaizzi method was used to analyze, summarize, and refine the interview data.ResultsThe dyadic care experiences of elderly individuals with disabilities and their caregivers can be summarized in terms of two themes. Theme 1 is dyadic pressure, which includes the following subthemes: (1) substantial objective burden; (2) dual negative experiences, i.e., the perceived low value of elderly individuals and low positive gains by caregivers; and (3) dyadic emotional transmission. Theme 2 is dyadic cooperative coping, which includes the following subthemes: (1) adjustment of family beliefs, including by giving meaning to stress, maintaining a positive outlook toward the future and ensuring spiritual sustentation; (2) changes in family patterns, including flexible adjustment of family patterns and multichannel utilization of social resources; and (3) improvement of family communication, including effective information transmission, rational emotional expression and emotional connection, and cooperation to solve and prevent problems.ConclusionElderly individuals with disabilities and their family caregivers face multiple physical, psychological, and social difficulties and demands during daily care, in which context negative experiences exert influence on this dyad. They collaborate to exhibit family resilience via the adaptation and improvement of family beliefs, family patterns and family communication. The family as a unit expends a great deal of effort to adapt to conditions of stress in the context of caring and shows family resilience, which is closely related to the family's cultural background and community situation. Dyadic resilience-based interventions can be developed based on core elements found by this study.

On the Integration of Sense and Reason in the Relation Between Science and Art—Take the Influence of Mathematical Form on Art Design as an Example

Both science and art are the cornerstones of the development of human civilization. The former writes a rational chapter, while the latter describes a perceptual blueprint. It is precisely for the sake that the integrity of human civilization and human beings themselves are the coexistence of rationality and perception that science and art are interdependent and mutually reinforcing. Taking the influence of mathematical form on art design as an example, this paper expresses the dialectical relationship between science and art in a concrete way, and tries to explore how to use the relationship between science and art to convey the rational and perceptual connotations more accurately. This paper mainly consists of five parts: the first part is the preface, which introduces the background, content and significance of this study; the second part is the summary of research methods and their use; the third part is the display of the results of the selected case analysis, which is divided into the beauty of symmetry and the beauty of geometric figures; the fourth part is from the aesthetic characteristics and uses. The fifth part is in view of the results of the analysis to provide suggestions for the rational and emotional expression of modern design, and put forward the feasible direction of follow-up research.

Sustainable Learning, Cognitive Gains, and Improved Attitudes in College Algebra Flipped Classrooms

To respond to global issues positively, education systems in higher education institutions play a significant role in empowering learners as well as promoting sustainable development goals. By implementing curricula that cultivate cross-cutting and transversal key competencies for sustainability, such as critical thinking, problem-solving, and collaboration, we prepare our pupils to become sustainability citizens, who not only sustain learning throughout their lives in various circumstances and across different disciplines but also engage constructively and responsibly toward any future world’s challenges through their dispositions, strategies, and skills. One such sustainable teaching methodology is known as the flipped classroom, an active-learning, student-centered, flexible, and multidimensional pedagogy. Our objective is to investigate the effect of such pedagogy on learners’ academic achievement and their attitude toward mathematics using both quantitative and qualitative methods. We cultivated sustainable learning in mathematics education for college freshmen (n=55) by exposing them to both the conventional teaching method (CTM) and flipped classroom pedagogy (FCP). By splitting them into control and experimental groups alternately (n1=24, n2=31) and by selecting the four most challenging topics in college algebra, we measured their cognitive gains quantitatively via a sequence of pre- and post-tests. The topics are factorization, rational expressions, radical operations, and applied problems. Both groups improved academically over time across all these four topics with statistically very significant outcomes (p&lt;0.001). Although they were not always statistically significant (p&gt;0.05) in some topics, the post-test results suggest that generally, the FCP trumps the CTM in cognitive gains, except for the first topic on factorization, where the opposite is true with a very statistically significant mean difference (p&lt;0.001). By examining non-cognitive gains qualitatively, we analyzed the students’ feedback on the FCP and their responses to a perception inventory. The finding suggests a favorable response toward the FCP with primary improvements in the attitudes toward mathematics and increased levels of cooperation among students. Since these students are so happy to have control of their own learning, they were more relaxed, motivated, confident, active, and responsible in learning under the FCP. We are confident that although this study is relatively small in scale, it will yield incremental and long-lasting effects not only for the learners themselves but also for other role-takers in education sectors who aspire in nurturing sustainable long-life learning and achieving sustainable development goals successfully.

Irreducible polynomials from a cubic transformation

Let R(x)=g(x)/h(x) be a rational expression of degree three over the finite field Fq. We count the irreducible polynomials in Fq[x], of a given degree, that have the form h(x)deg⁡f⋅f(R(x)) for some f(x)∈Fq[x]. As an example of application of our results, we recover the number of irreducible transformation shift registers of order three, which were computed by Jiang and Yang in 2017.

A robust class of linear recurrence sequences

We introduce a subclass of linear recurrence sequences which we call poly-rational sequences because they are denoted by rational expressions closed under sum and product. We show that this class is robust by giving several characterisations: polynomially ambiguous weighted automata, copyless cost-register automata, rational formal series, and linear recurrence sequences whose eigenvalues are roots of rational numbers.

An Application to Fixed-Point Results in Tricomplex-Valued Metric Spaces Using Control Functions

In the present work, we establish fixed-point results for a pair of mappings satisfying some contractive conditions on rational expressions with coefficients as point-dependent control functions in the setting of tricomplex-valued metric spaces. The proven results are extension and generalisation of some of the literature’s well-known results. We also explore some of the applications to our key results.

Jet schemes of quasi-homogeneous hypersurfaces and motivic monodromy conjecture for isolated quasi-homogeneous hypersurface singularities

Let $k$ be a field. Let $m\in\mathbf{N}_{>0}$ be a positive integer. Let $f\in k[x_1,\ldots,x_m]$ be a polynomial with degree $d\geq 1$ and associated hypersurface $H:=H(f):=\mathrm{Spec}(k[x_1,\ldots,x_m]/\langle f\rangle)$. In this article, we firstly provide a structure property of the weighted-homogeneity of $f$ in terms of the jet schemes ${\mathscr{L}_{H}}$ of $H$. As a by-product, we deduce from this property a new and very \linebreak effective method for the computation of the motivic Poincaré power series $P_H(T):=\sum_{n\geq 0} [\mathscr{L}_{n}(H)]T^n\in K_0(\mathrm{Var}_k)[[T]]$ associated with a homogeneous hypersurface $H$ with a single isolated singularity at the origin $\frak o$ (and more generally with a specific class of isolated quasi-homogeneous hypersurface singularities). With this point of view we obtain various consequences. For the considered class of varieties, our method provides a characteristic-free proof of the rationality of $P_H(T)$ which does not use motivic integration nor the existence of resolutions of singularities; we obtain a precise description of the numerator and the possible poles in the rational expression of $P_H(T)$; when the field is assumed to be of characteristic zero, this allows us to prove the validity of the motivic monodromy conjecture.

The awareness of difficulties in solving rational inequality and a solution proposal

This research aimed to determine the difficulties that the students experience in inequality solutions that contain inequality in general and rational (proportional) expressions, and to solve these difficulties with an activity. Totally 108 students, who were enrolled in the Department of Mathematics and Science Education, consisted respectively of 43 in the 2015-2016, 32 in the 2016-2017, and 33 in the 2017-2018 academic year, participated in the research. It was started with an activity to make students realize the difficulties they experienced and become aware of the stages which they had difficulty. After the activity, the difficulties, and the stages that students had difficulties were determined. At that point, they were informed about the solutions for the difficulties they faced and shown a road map for coping with the stages they had difficulties. At the end of the research, the rational inequality questions were asked to the students in the mid-term and/or final exams, and it was observed that the majority of students did not experience any of the problems which they had experienced before the activity. Another result of the study was that the students had less difficulty in the inequalities related to the concept of greatest integer, which they received only in university education.