Conjugate Functions Research Articles

Integrative and Conjugative Element ICETh1 Functions as a Pangenomic DNA Capture Module in Thermus thermophilus

Transjugation is an unconventional conjugation mechanism in Thermus thermophilus (Tth) that involves the active participation of both mating partners, encompassing a DNA secretion system (DSS) in the donor and an active natural competence apparatus (NCA) in the recipient cells. DSS is encoded within an integrative and conjugative element (ICETh1) in the strain Tth HB27, whereas the NCA is constitutively expressed in both mates. Previous experiments suggested the presence of multiple origins of transfer along the genome, which could generate genomic mosaicity among the progeny. Here, we designed transjugation experiments between two closely related strains of Tth with highly syntenic genomes, containing enough single nucleotide polymorphisms to allow precise parenthood analysis. Individual clones from the progeny were sequenced, revealing their origin as derivatives of our ICETh1-containing intended “donor” strain (HB27), which had acquired separate fragments from the genome of the ICETh1-free HB8 cells, which are our intended recipient. Due to the bidirectional nature of transjugation, only assays employing competence-defective HB27 derivatives as donors allowed the recovery of HB8-derived progeny. These results show a preference for a retrotransfer mechanism in transjugation in ICETh1-bearing strains, supporting an inter-strain gene-capture function for ICETh1. This function could benefit the donor-capable host by facilitating the acquisition of adaptive traits from external sources, ultimately increasing the open pangenome of Thermus, maximizing the potential repertoire of physiological and phenotypical traits related to adaptation and speciation.

Analysis of a Regulated Cascode Cross Couple Power Amplifier

The input impedance of a regulated cascode cross couple amplifier is derived. The frequency response of the input impedance polynomial form can be plotted with MATLAB. From the polynomial form of the input impedance of the proposed circuit, it can be transformed by substitute complex frequency s with jω into the polynomial form equation. After that, this function can be grouped into a symbolic real and a symbolic imaginary form. The next step in derivation is to multiply this function with a complex conjugate function of the symbolic complex form of the input impedance. The last step is to plot a real and an imaginary part as a function of the input frequency so that the power amplifier can be matching with the various matching circuit according to the condition of the maximum power transfer.

Perturbation of Image and conjugate duality for vector optimization

<p style='text-indent:20px;'>This paper aims at employing the image space approach to investigate the conjugate duality theory for general constrained vector optimization problems. We introduce the concepts of conjugate map and subdifferential by using two types of maximums. We also construct the conjugate duality problems via a perturbation method. Moreover, the separation condition is proposed by means of vector weak separation functions. Then, it is proved to be a new sufficient condition, which ensures the strong duality theorem. This separation condition is different from the classical regular conditions in the literature. Simultaneously, the application to a nonconvex multi-objective optimization problem is shown to verify our main results.</p>

Look at Tempered Subdiffusion in a Conjugate Map: Desire for the Confinement.

The Laplace distribution of random processes was observed in numerous situations that include glasses, colloidal suspensions, live cells, and firm growth. Its origin is not so trivial as in the case of Gaussian distribution, supported by the central limit theorem. Sums of Laplace distributed random variables are not Laplace distributed. We discovered a new mechanism leading to the Laplace distribution of observable values. This mechanism changes the contribution ratio between a jump and a continuous parts of random processes. Our concept uses properties of Bernstein functions and subordinators connected with them.

A special approach to derive new formulas for some special numbers and polynomials

By applying Laplace differential operator to harmonic conjugate components of the analytic functions and using Wirtinger derivatives, some identities and relations including Bernoulli and Euler polynomials and numbers are obtained. Next, using the Legendre identity, trigonometric functions and the Dirichlet kernel, some formulas and relations involving Bernoulli and Euler numbers, cosine-type Bernoulli and Euler polynomials, and sine-type Bernoulli and Euler polynomials are driven. Then, by using the generating functions method and the well-known Euler identity, many new identities, formulas, and combinatorial sums among the Fibonacci numbers and polynomials, the Lucas numbers and polynomials, the Chebyshev polynomials, and Bernoulli and Euler type polynomials are given. Finally, some infinite series representations for these special numbers and polynomials and their numerical examples are presented.

On The Chinese Checkers Spherical Inversions in Three Dimensional Chinese Checkers Space

In this paper, we study an inversion with respect to a Chinese checkers sphere in the three dimensional Chinese Checkers space, and prove several properties of this inversion. We also study cross ratio, harmonic conjugates and the inverse images of lines, planes and Chinese Checkers spheres in three dimensional Chinese Checkers space.

Grothendieck Theorem for Some Uniform Algebras and Modules Over Them

Under certain additional assumptions, it is proved that a w∗-closed subalgebra X of L∞(μ) (more generally, a w∗-closed module over X) verifies the Grothendieck theorem. The assumptions in question imitate a property of the classical harmonic conjugation operator but are less restrictive than it is usual in similar settings. Specifically, μ may fail to be multiplicative on X, etc.

A Universal and Structured Way to Derive Dual Optimization Problem Formulations

The dual problem of a convex optimization problem can be obtained in a relatively simple and structural way by using a well-known result in convex analysis, namely Fenchel’s duality theorem. This alternative way of forming a strong dual problem is the subject of this paper. We recall some standard results from convex analysis and then discuss how the dual problem can be written in terms of the conjugates of the objective function and the constraint functions. This is a didactically valuable method to explicitly write the dual problem. We demonstrate the method by deriving dual problems for several classical problems and also for a practical model for radiotherapy treatment planning, for which deriving the dual problem using other methods is a more tedious task. Additional material is presented in the appendices, including useful tables for finding conjugate functions of many functions.

Optimal control of higher order viable differential inclusions and duality

The paper is devoted to the duality of the Mayer problem for -th order viable differential inclusions with endpoint constraints, where is an arbitrary natural number. Thus, this paper for constructing the dual problems to viable differential inclusions of any order with endpoint constraints can make a great contribution to the modern development of optimal control theory. For this, using locally conjugate mappings in the form of Euler–Lagrange type inclusions and transversality conditions, sufficient optimality conditions are obtained. It is noteworthy that the Euler–Lagrange type inclusions for both primary and dual problems are ‘duality relations’. To demonstrate this approach, some semilinear problems and polyhedral optimization with fourth order differential inclusions are considered. These problems show that sufficient conditions and dual problems can be easily established for problems of a reasonable order.

Approximations of Conjugate Functions by Partial Sums of Conjugate Fourier Series with Respect to a Certain System of Chebyshev – Markov Algebraic Fractions

Approximations of Conjugate Functions by Partial Sums of Conjugate Fourier Series with Respect to a Certain System of Chebyshev – Markov Algebraic Fractions

A Mixed-method Study of Individual, Couple, and Parental Functioning During the State-regulated COVID-19 Lockdown in Spain.

During the recent COVID‐19 outbreak in Spain, we explored the individual and relational well‐being of people confined together with their partners and/or children during the first 3 weeks of state‐regulated lockdown. Adults 18 years or older (N = 407) completed an online survey that included demographic, household, and employment information along with standardized measures of psychological distress (State‐Trait Anxiety and Beck Depression) and relationship functioning—either the Dyadic Adjustment Scale if there were no children in the household or a Basic Family Relations Evaluation Questionnaire (CERFB) measuring conjugal, parental, and coparental functions. Qualitative analyses of responses to an open‐ended question about perceived changes in couple or family dynamics during lockdown revealed nine specific themes comprising two overarching categories: relational improvement and deterioration. The overall prevalence of improvement themes (61.7%) exceeded deterioration themes (41.0%), with increased (re)connection and conflict atmosphere cited most often. Quantitative analyses found elevated levels of state anxiety but not trait anxiety or depression during lockdown. Consistent with the qualitative results, couples having no children at home reported high levels of dyadic adjustment, but with children present CERFB parental functioning exceeded conjugal functioning, a pattern sometimes associated with child triangulation into adult conflicts. Although correlates of psychological distress (e.g., unemployment, perceived economic risk) were relatively stable across subgroups, predictors of relationship functioning varied substantially with household/parental status (e.g., telecommuting and employment facilitated conjugal functioning only for couples with children).

Novel hybrid robust method for uncertain reliability analysis using finite conjugate map

Due to the limitation of measured data, the random and epistemic uncertainties must be simultaneously handled for the reliability analysis of curvilinear aircraft stiffened panels with multiple cutouts. A hybrid iterative conjugate first-order reliability method (CFORM) and adaptive dynamical harmony search (ADHS) optimization are developed for fuzzy reliability analysis (FRA) of stiffened panels. The proposed global level performs fuzzy analysis using ADHS, while the local level is utilized for reliability evaluation using efficient FORM. In ADHS, two adjusting procedures are implemented to update the new positions of reliability index bounds with dynamical parameters Due to the computational burden of fuzzy reliability analysis with robust iterative formula, a conjugate FORM is applied using finite-step size, which is formulated by applying the Armijo rule. A limited conjugate scalar factor is utilized to determine the conjugate nonlinear describe map. The proposed conjugate formula is examined by various FORM formulas. The fuzzy reliability index is obtained using alpha level set-based ADHS in terms of extracted results by conjugate FORM for stiffened panels. Furthermore, by the sensitivity measure of the fuzzy reliability index, boundaries of uncertainty interval for stiffener heights and thicknesses of the panel were proposed. Moreover, the influences of different stiffener height, design load, stiffener thickness, and skin thickness on buckling mode were discussed. Survey results demonstrated that the proposed FRA is more accurate to handle epistemic uncertainties of curvilinear aircraft stiffened panels than the classic reliability method-based FORM. The conjugate reliability method provides robust and efficient results compared to the modified iterative reliability methods.

Simulation and Analysis on Tooth Meshing Ease-Off Surface of Gears Based on Polynomial Topology Modification

Based on the principles of common-generating conjugation mapping of pinion-rank-gear meshing, the constructing of ease-off surface has been done by means of the topology modification of the 4-order polynomial surface. The simulation method of tooth surface mesh is purposed based on the ease-off surface. By analyzing topological structure characteristics of ease-off surface such as modification gradient curves, contact line-off and contact path-off, the meshing characteristics such as the contact area, the contact line and transmission error are determined. It is stated on the interaction relations of coefficients of the 4-order polynomial to the topological construction of surface. The methods for reconstruction and analysis of ease-off surface with considering axis misalignments are presented by the direct transformation of coordinate systems. Taking the topological construction of four kinds of surfaces as examples, characteristics parameters such as modification gradient of tooth surface, contact path and transmission errors are simulated. They are expounded on the corresponding parameters of controlling form and adjusting methods for tooth surface. These methods take goals of adjusting-modification and controlling-property for tooth surface mesh. It is improved and developed the meshing analysis method of ease-off surface of tooth. The presented method is liable to provide the basis data for the further loaded contact analysis of complicated tooth surface and the more direct technical for the 3-D topological optimization of tooth surface.

Regularity conditions and Farkas-type results for systems with fractional functions

This paper deals with some new versions of Farkas-type results for a system involving cone convex constraint, a geometrical constraint as well as a fractional function. We first introduce some new notions of regularity conditions in terms of the epigraphs of the conjugate functions. By using these regularity conditions, we obtain some new Farkas-type results for this system using an approach based on the theory of conjugate duality for convex or DC optimization problems. Moreover, we also show that some recently obtained results in the literature can be rediscovered as special cases of our main results.

Pointwise approximation of modified conjugate functions by matrix operators of their Fourier series with the use of some parameters

We extend and generalize the results of Xh. Z. Krasniqi [Acta Comment. Univ.Tartu. Math. 17 (2013), 89-101] and the authors [Acta Comment. Univ. Tartu.Math. 13 (2009), 11-24], [Proc. Estonian Acad. Sci. 2018, 67, 1, 50--60] aswell the jont paper with M. Kubiak [Journal of Inequalities and Applications(2018) 2018:92]. We consider the modified conjugate function $\widetilde{f}%_{r}$ for $2\pi /\rho $--periodic function $f$ . Moreover, the measure ofapproximations depends on \textbf{\ }$\mathbf{\rho }$\textbf{ - }differencesof the entries of matrices defined the method of summability.

Structure and Evolution of Acinetobacter baumannii Plasmids.

Acinetobacter baumannii is an emergent bacterial pathogen that provokes many types of infections in hospitals around the world. The genome of this organism consists of a chromosome and plasmids. These plasmids vary over a wide size range and many of them have been linked to the acquisition of antibiotic-resistance genes. Our bioinformatic analyses indicate that A. baumannii plasmids belong to a small number of plasmid lineages. The general structure of these lineages seems to be very stable and consists not only of genes involved in plasmid maintenance functions but of gene sets encoding poorly characterized proteins, not obviously linked to survival in the hospital setting, and opening the possibility that they improve the parasitic properties of plasmids. An analysis of genes involved in replication, suggests that members of the same plasmid lineage are part of the same plasmid incompatibility group. The same analysis showed the necessity of classifying the Rep proteins in ten new groups, under the scheme proposed by Bertini et al. (2010). Also, we show that some plasmid lineages have the potential capacity to replicate in many bacterial genera including those embracing human pathogen species, while others seem to replicate only within the limits of the Acinetobacter genus. Moreover, some plasmid lineages are widely distributed along the A. baumannii phylogenetic tree. Despite this, a number of them lack genes involved in conjugation or mobilization functions. Interestingly, only 34.6% of the plasmids analyzed here possess antibiotic resistance genes and most of them belong to fourteen plasmid lineages of the twenty one described here. Gene flux between plasmid lineages appears primarily limited to transposable elements, which sometimes carry antibiotic resistance genes. In most plasmid lineages transposable elements and antibiotic resistance genes are secondary acquisitions. Finally, broad host-range plasmids appear to have played a crucial role.

The influence of carboxylate moieties for efficient loading and pH-controlled release of doxorubicin in Fe3O4 magnetic nanoparticles

One of the significant challenges in a nanoparticles-based anticancer drug delivery system for cancer therapy application is to design nanoparticles with specific functionality for efficient drug conjugation and release. In the present study, different carboxylate molecules, i.e., succinic acid (SA), ascorbic acid (AA), and citric acid (CA), were used as surface modifiers for delivery of an anticancer drug, doxorubicin (DOX), using Fe3O4 magnetic nanoparticles (MNPs). Here, a simple one-pot co-precipitation method was successfully used to fabricate monodisperse and uniform carboxylates functionalized Fe3O4 nanoparticles with excellent superparamagnetic properties and colloidal stabilities. Based on the result, the as-prepared MNPs exhibited high drug loading due to the formation of intermolecular forces between DOX and carboxylates moieties or MNPs surface. Besides, the release of the loaded DOX could quickly be released by simply reducing the pH of the suspension. However, it was observed that both loading efficiency and release of DOX were significantly affected by the type of carboxylate moieties. Finally, in vitro MTT assay of HeLa cell lines also revealed that the as-prepared DOX-loaded nanoparticles were able to induce the death of the cancer cell efficiently.

Structural Basis for Targeting T:T Mismatch with Triaminotriazine-Acridine Conjugate Induces a U-Shaped Head-to-Head Four-Way Junction in CTG Repeat DNA.

The potent DNA-binding compound triaminotriazine-acridine conjugate (Z1) functions by targeting T:T mismatches in CTG trinucleotide repeats that are responsible for causing neurological diseases such as myotonic dystrophy type 1, but its binding mechanism remains unclear. We solved a crystal structure of Z1 in a complex with DNA containing three consecutive CTG repeats with three T:T mismatches. Crystallographic studies revealed that direct intercalation of two Z1 molecules at both ends of the CTG repeat induces thymine base flipping and DNA backbone deformation to form a four-way junction. The core of the complex unexpectedly adopts a U-shaped head-to-head topology to form a crossover of each chain at the junction site. The crossover junction is held together by two stacked G:C pairs at the central core that rotate with respect to each other in an X-shape to form two nonplanar minor-groove-aligned G·C·G·C tetrads. Two stacked G:C pairs on both sides of the center core are involved in the formation of pseudo-continuous duplex DNA. Four metal-mediated base pairs are observed between the N7 atoms of G and CoII, an interaction that strongly preserves the central junction site. Beyond revealing a new type of ligand-induced, four-way junction, these observations enhance our understanding of the specific supramolecular chemistry of Z1 that is essential for the formation of a noncanonical DNA superstructure. The structural features described here serve as a foundation for the design of new sequence-specific ligands targeting mismatches in the repeat-associated structures.

Riesz’s Theorem for Lumer’s Hardy Spaces

In this note, we obtain a version of the well-known Riesz’s theorem on conjugate harmonic functions for Lumer’s Hardy spaces on arbitrary domains Ω: If a real-valued harmonic function has a harmonic conjugate V on Ω (i.e., a real-valued harmonic function such that U + iV is analytic on Ω), then U + iV also belongs to , and for the normalized conjugate we have the norm estimate , with the best possible constant.

A dual approach for optimal algorithms in distributed optimization over networks

We study dual-based algorithms for distributed convex optimization problems over networks, where the objective is to minimize a sum of functions over in a network. We provide complexity bounds for four different cases, namely: each function is strongly convex and smooth, each function is either strongly convex or smooth, and when it is convex but neither strongly convex nor smooth. Our approach is based on the dual of an appropriately formulated primal problem, which includes a graph that models the communication restrictions. We propose distributed algorithms that achieve the same optimal rates as their centralized counterparts (up to constant and logarithmic factors), with an additional optimal cost related to the spectral properties of the network. Initially, we focus on functions for which we can explicitly minimize its Legendre–Fenchel conjugate, i.e. admissible or dual friendly functions. Then, we study distributed optimization algorithms for non-dual friendly functions, as well as a method to improve the dependency on the parameters of the functions involved. Numerical analysis of the proposed algorithms is also provided.