Fundamental Solution Research Articles

In vitro synthesis and biochemical characterization of acyl-homoserine lactone synthase and its deletion mutant.

Quorum sensing can induce density-dependent gene expressions that cause various problems. For quorum-sensing inhibition, fundamental solutions such as gene manipulation are required, and acyl-homoserine lactone synthase (AHL synthase), which synthesizes the universal quorum-sensing signal of gram-negative bacteria, can be used as a target. In this study, researchers synthesized His-tagged AHL synthase and its deletion mutant that lacks the active site and compared their biochemical characteristics. His-YpeI, the 6x His-tagged AHL synthase of Serratia fonticola, and His-ΔYpeI, its deletion mutant, were designed, and their property conservation were examined using in silico projection tools. For in vitro synthesis of enzymes, the His-YpeI CFPS template was synthesized by in vitro gene synthesis, and the His-ΔYpeI CFPS template was obtained by deletion PCR. CFPS was performed and the products were purified with the 6x His-tag. The enzymes' properties were compared using an enzymatic assay. The bioinformatic analysis confirmed the conservation of biochemical properties between 6x His-tagged and untagged enzymes, including helix-turn-helix interactions, hydropathy profiles, and tertiary structure between His-YpeI and YpeI and between His-ΔYpeI and ΔYpeI. His-YpeI and His-ΔYpeI synthesized by CFPS were found to have the expected molecular weights and demonstrated distinct differences in enzyme activity. The analyzed enzymatic constants supported a significant decrease in substrate affinity and reaction rate as a result of YpeI's enzyme active site deletion. This result showed that CFPS could be used for in vitro protein synthesis, and quorum sensing could be inhibited at the enzymatic level due to the enzyme active site's deletion mutation.

Breaking Down Data Sharing Barrier of Smart City: A Digital Twin Approach

The smart city aims to enhance the efficacy of urban management and improve the quality of citizen life. This however faces a fundamental difficulty due to the inadequate data sharing among social entities, which has become one of the key barriers to the in-depth development of smart city, making wasted information resources and application silos ubiquitous. As an emerging communication paradigm, the digital twin network (DTN) has the potential to eliminate the data-sharing barrier in smart cities. By mapping the social physical entities (PEs) in the smart city to digital virtual agents, namely data twins (DTs), valuable data can be directly shared among the DTs over DTN without physical constraints, and form decisions that feedback and guide the operations of PEs. In this article, we explore the role of DTN in supporting the smart city and promoting data-sharing construction. We first introduce the basic concepts related to DTN and propose the architecture of DTN-enabled smart city. The key features of the DTN-enabled smart city are then discussed with an emphasis on the security and privacy issues with fundamental solutions around data sharing in the DTN-enabled smart city. As a case study, we investigate data sharing in the DTN-enabled smart city and design a secure and fair data-sharing mechanism. Finally, we propose open challenges for achieving a more reliable DTN-enabled smart city.

SOLUTIONS OF SOME INTEGRAL EQUATIONS OF THE SECOND KIND

The article examines the solutions of some integral equations of the second kind. Such equations arise when using Levi's method to construct a fundamental solution of the Cauchy problem for a degenerate equation of the Kolmogorov type. The equation may also contain a degeneracy on the initial hyperplane. The coefficients of this equation are bounded in the group of principal terms and ones are increasing functions in the group of lowest terms. The considered classes of kernels of integral equations make it possible to preserve the function that determines the growth of the coefficients of the parabolic equation when evaluating the resolvent. In the evalutions of the kernels of integral equations, there are evaluation functions that arise when constructing the corresponding fundamental solution, and fundamental solution of the Cauchy problem of the model equation with constant coefficients.

Changing Pattern of Women Empowerment in Bangladesh: An Administrative Perspective

The pattern of women’s empowerment has many features over the years in post-colonial periods and after the inception of Bangladesh’s Independence in terms of administrative views. The study has been accomplished through qualitative methodology by analyzing reviewed journals (secondary sources). The study’s objectives are to discover the changing pattern of women’s empowerment through government initiatives in different periods in Bangladesh and to critically analyze the gaps in women’s empowerment to articulate the current positions of women in Bangladesh. The study’s findings have been organized by the government’s initiatives over the periods and the fundamental challenges and solutions of women’s empowerment in Bangladesh. The governments’ initiatives have been classified into three periods. Each period was organized by the significant initiatives of the government and the conditions of women’s empowerment at that time. Recognizing women’s empowerment used two primary determinants: adult literacy rate and participation in the making process of women, respectively. The study suggests that the concerned authority needs to update its administrative approaches to Change the Pattern of Women Empowerment in Bangladesh.

Sliding friction of a pillar array interface: part II, contact mechanics of single pillar pairs.

Insects and small animals often utilize structured surfaces to create friction during their movements. These surfaces typically consist of pillar-like fibrils that interact with a counter surface. Understanding the mechanical interaction between such surfaces is crucial for designing structured surfaces for engineering applications. In the first part of our study, we examined friction between poly(dimethylsiloxane) (PDMS) samples with surfaces patterned with pillar-arrays. We observed that sliding between these surfaces occurs through the interfacial glide of dislocation structures. The frictional force that resists this dislocation glide is a result of periodic single pillar-pillar contact and sliding. Hence, comprehending the intricate interaction between individual pillar contacts is a fundamental prerequisite for accurately modeling the friction behavior of the pillar array. In this second part of the study, we thoroughly investigated the contact interaction between two pillars located on opposite sides of an interface, with different lateral and vertical offsets. We conducted experiments using PDMS pillars to measure both the reaction shear and normal forces. Contact interaction between pillars was then studied using finite element (FE) simulations with the Coulomb friction model, which yielded results that aligned well with the experimental data. Our result offers a fundamental solution for comprehending how fibrillar surfaces contact and interact during sliding, which has broad applications in both natural and artificial surfaces.

APPLICATION OF THE POTENTIAL THEORY TO SOLVING A MIXEDPROBLEM FOR A MULTIDIMENSIONAL ELLIPTIC EQUATION WITHONE SINGULAR COEFFICIENT

Potential theory has played a paramount role in both analysis and computation for boundary value problems for elliptic equations. In the middle of the last century, a potential theory was constructed for a two-dimensional elliptic equation with one singular coefficient. In the study of potentials, the properties of the fundamental solutions of the given equation are essentially and fruitfully used. At the present time, fundamental solutions of a multidimensional elliptic equation with one degeneration line are already known. In this paper, we investigate the double- and simple-layer potentials for this kind of elliptic equations. Results from potential theory allow us to represent the solution of the boundary value problems in integral equation form. By using some properties of Gaussian hypergeometric function, we prove limiting theorems and derive integral equations concerning a densities of the double- and simple-layer potentials. The obtained results are applied to find a solution of the mixed problem for the multidimensional singular elliptic equation in the half-space

Asymptotics of Fundamental Solutions of Parabolic Problems

В заметке излагаются способы построения асимптотики фундаментального решения параболических уравнений типа Фоккера-Планка-Колмогорова с малым параметром как при при малых, так и конечных положительных временах. Библиография: 12 названий.

THE NARROW-BAND FILTER BASED ON A MAGNETOPHOTONIC CRYSTAL INVOLVING LAYERS WITH HYPERBOLIC DISPERSION LAWS

Subject and Purpose. Narrow-band filters are among the basic components of modern communication systems, instruments for spectros- copy, high-sensitivity sensors, etc. Photonic crystal structures open up broad possibilities for creating compact-sized, narrow-band filters in the optical and terahertz ranges. Tuning of spectral characteristics of photonic crystal filters is usually carried out through introduction of certain elements into their structure that are sensitive to external electric and magnetic fields. This work has been aimed at investigating electrodynamic characteristics of one-dimensional magnetophotonic crystals with structural layers characterized by "hyperbolic" disper- sion, and suggesting a multichannel, narrow-band filter on their base. Methods and Methodology. The dispersion equation for excitations in an infinite magnetophotonic crystal has been obtained within the framework of the Floquet-Bloch theory, with the use of fundamental solutions of Hill’s equation. The transfer matrix approach has been used to obtain an analytical expression for the transmission coefficient. Results. The band diagram of the one-dimensional magnetophotonic crystal has been analyzed for the case where one of the layers on the structure’s spatial period is characterized by a hyperbolic dispersion law. The areas of existence of surface wave regimes have been found for such layers for the case of normal incidence of the wave upon the finite-seized magnetophotonic crystal. Frequency dependences of the transmission coefficient are characterized by a set of high-Q resonant peaks relating to Fabry-Perot resonances in a periodic struc- ture of finite length. Conclusions. Application of a finite-seized, one-dimensional magnetophotonic crystal is considered as of a means forachieving mul- tichannel optical filtering and formation of a frequency comb. Expressions for the dispersion equation and transmission coefficient have been obtained within the framework of the Floquet-Bloch theory and with the use of the transfer matrix. The feasibility of surface mode excitation has been shown for gyrotropic layers of the periodic structure characterized by a hyperbolic dispersion law, for the case of nor- mal incidence upon the magnetophotonic crystal. The spectral response of the filter contains narrow-band peaks with a high transmission efficiency. By increasing the number of the structure’s periods it is possible to form a frequency comb, which effect can be useful for appli- cations in metrology and modern optical communication systems.

A superstable sandwich-type composite of a single-benzene-based fluorophore and chitosan as a fluorescent authentication barcode.

Management of diseases through medication accounts for the largest portion of treatment, with people worldwide relying on a variety of medicines to treat and prevent minor to severe diseases in modern society. However, the recent increased use of counterfeit medicines rather than certified medication has emerged as a serious social concern. This study introduces a new hybrid material, named SBBF-chitosan (SC), which integrates a single-benzene-based fluorophore (SBBF) and chitosan, serving as a fluorescence-based authentication barcode for certified medication. The synthesis and characterization of SC, along with an analysis of its photophysical properties, were systematically conducted. SC demonstrated bright emission with high stability under various environmental conditions. In vitro analyses and in vivo animal experiment results further indicated the safety of SC for oral intake, even when directly incorporated into medicines. We are confident that this newly developed formulation SC provides a fundamental solution to address the challenges posed by counterfeit medicines, thereby safeguarding medication authenticity.

«ВИТАФИЛД» – функциональное восстановление ресурсов человеческого организма

The human body contains nearly all the chemical elements of D.I. Mendeleev’s table. Their interaction affects the functioning of all organs and systems, and the state of human health is directly related to the body’s ability to restore and maintain the balance of chemical elements. One of the fundamental solutions for the complete restoration of the balance of the body, all of its parameters, functions of its organs and systems is the use of a corrector in the form of natural microorganisms bacillus subtilis, which trigger the body’s natural ability to self-heal, and which form the basis of Vitafield products.

Mean value formulas for classical solutions to some degenerate elliptic equations in Carnot groups

<p style='text-indent:20px;'>We prove surface and volume mean value formulas for classical solutions to uniformly elliptic equations in divergence form with Hölder continuous coefficients. The kernels appearing in the integrals are supported on the level and superlevel sets of the fundamental solution relative the adjoint differential operator. We then extend the aforementioned formulas to some subelliptic operators on Carnot groups. In this case we rely on the theory of finite perimeter sets on stratified Lie groups.</p>

Numerical conformal mapping for underground unlined tunnels with arbitrary shapes based on Symm’s method

Conformal mapping technique is important in theoretical analysis and numerical computation for the fields of stress and displacement. In general, a unlined tunnel with arbitrary shape has no analytical solution for conformal mapping. Therefore, the study of numerical method for conformal mapping has great significance. The basic functions of numerical conformal mapping are given based on Symm’s method in this paper. Furthermore, the inverse mapping functions were deduced according to the relationships between the boundary nodes in physical and mapped plane. Compared to the other numerical methods, the presented method has some advantages such that, it is simple in concept to be understood, and can give the mapping function without iteration process. The method can be used to the forward and inverse numerical conformal mappings for multiple underground unlined tunnels with arbitrary shapes in finite and infinite domains. With the help of method of fundamental solutions (MFS), the interpolation equations were proposed for multiple underground unlined tunnels with arbitrary shapes. Finally, several numerical examples for the groups of U-shaped and rectangle tunnels have been given to verify the effectiveness of this method. The numerical results can convergent to real cases, which show that the proposed method has the properties of good accuracy and strong adaptability.

The political ideology education for students at Viet Nam National University Ho Chi Minh City in the current context: Current situation and some key solutions

Political ideology education for students in higher education institutions plays a pivotal role in nurturing their qualities and personalities, as well as endowing them with a scientific worldview and a correct methodology. This education contributes significantly to shaping generations of students, who possess both political integrity and professional competence, capable of undertaking substantial responsibilities in a landscape, where the nation enjoys numerous advantages but also faces hidden difficulties and challenges. Drawing from the research conducted on the political ideology education for students at Viet Nam National University Ho Chi Minh City, this article examines the present state of this endeavor from the two perspectives: the attained outcomes and the remaining challenges. By analyzing the current context, the article puts forward several key solutions aimed at enhancing the efficacy of this education within the contemporary pivotal framework for the country's development. The research findings show that the political ideology education for students at Viet Nam National University Ho Chi Minh City is consistently regarded as a crucial, strategic, and enduring task. It receives ample attention and implementation from the entire political apparatus, manifesting in a variety of approaches that blend tradition with modernity. Consequently, this educational effort has achieved depth and fortified its efficacy. However, notwithstanding its accomplishments, recent developments have revealed certain shortcomings and constraints stemming from both subjective and objective factors. Hence, there is a pressing need for fundamental solutions to augment the effectiveness of this education and align it more closely with the prevailing context.

GIS를 활용한 불법 주정차 핫스팟 분석

Illegal parking inhabits the convenience of transportation, threatens the safety of pedestrians, and worsens the emergency situation by acting as an obstacle. Each local government has made efforts in various ways, such as expanding the no-parking area and operation resident reporting systems for illegal parking, but it is not sufficient to resolve the illegal parking problem, with the many complaints related to the illegal parking in all complaints. Therefore, this study conducted spatial analysis to derive a solution to the illegal parking phenomenon based on the theory of evidence-based policing for crime prevention and interpreted the phenomenon by using Ratcliffe's hotspot matrix.
 Seongnam-si, Gyeonggi-do, ranked first in the number of illegal parking reports by district, and Jung-gu, Daegu-si, ranked first in the reports per area, were selected as study areas. As a result of executing Moran's I analysis, a methodology to ascertain spatial dependency for each area, revealed that both regions exhibited positive spatial dependency, indicating a spatial association with illegal parking incidents.
 Furthermore, Local Moran’s I analysis, a methodology that identifies areas with significant differences from the surrounding areas by setting the analysis scope locally, was conducted to understand the spatial and temporal distribution of hotspots where illegal parking occurs frequently.
 In Seongnam, hotspot areas with high reported volumes appear in large, distributed forms and scattered patterns throughout the city, exhibiting characteristics of spatial clustering and temporal concentration according to Ratcliffe's hotspot matrix. In addition, it was found that the hotspots were often adjacent to the parks, suggesting ways to fundamentally improve parking environment around the parks by activating the sharing of idle parking spaces in surrounding buildings, and encouraging citizens to participate voluntarily through logo-projectors.
 In Jung-gu, Daegu-si, the result presented that most hotspots from a cluster in Dongseong-ro, with a more concentrated temporal concentration, indicating spatial clustering and temporal acuteness based on Ratcliffe's hotspot matrix. Therefore, we propose concentrated patrols around the hotspot area during by time periods to persuade illegal parking vehicles. In particular, benchmarking the current flexible patrol system used by the police and utilizing optimal routes were suggested to ensure efficient patrols. Moreover, using intelligent CCTV was proposed to effectively enforce habitual areas.
 By applying the methods presented in this study, local governments can utilize valuable information for policy decision-making to facilitate efficient evidence-based policing activities and derive fundamental solutions to illegal parking issues.

The fundamental solution to □b on quadric manifolds with nonzero eigenvalues and null variables

The fundamental solution to □b on quadric manifolds with nonzero eigenvalues and null variables

공교육 정상화를 위한 교육활동 보호제도의 개선 방향

According to the recent media reports on the infringement of educational activities, there are serious concerns about whether our children are living in a safe and healthy environment. This is the worst situation in which not only teachers' classes but also life guidance in the class itself becoming almost impossible in serious cases. Why are we aware of the seriousness of infringement of teaching rights and discuss its improvements? This is because when an incident occurs, a situation in which normal educational activities are not carried out unfolds. This leads to a vicious cycle in which the majority of students' right to learn and human rights are hindered. In the future, social concerns about the seriousness of infringement of teaching authority and consensus on the importance of restoring teaching authority should be prioritized. However, separating the student group and the teaching group into opposing relationships and polarizing them in an ideological biased way or political logic cannot be a fundamental solution to this problem. The constitutional meaning of “right to study” is fading in the school field we are currently experiencing. In order to protect teaching rights, the government has been pursuing institutional and policy measures, but confusion in the educational field has not been resolved. It is clear that schools are spaces that require the publicity of education. Professionalism of teachers, and mutual respect and cooperation between educational subjects. Students, parents, and teachers should develop a cooperative relationship based on mutual esteem and human rights. The protection of teaching rights should be promoted realistically through the change of consciousness and policy supplementation of the educational subject. It should be known that all our students' right to learn is guaranteed and a pleasant school life can continue only when the educational environment is stabilized.

자애(Metta)명상과 ADHD 청소년의 또래 관계 개선에 관한 연관성 연구

This paper is a study that revealed that Metta meditation helps improve peer relationships among young people with ADHD (Attention Deficit Hyperactivity Disorder). I hope that young people living with ADHD symptoms can recognize differences in viewpoints of people around them with a negative perspective, recognize differences for themselves through psychological and emotional stability by combining medication and Buddhist meditation to solve external problems, and they will live a happy life as a member of society by improving their self-esteem and developing interpersonal skills by utilizing their strengths and weaknesses with people around them. 
 Its purpose is to find out how Buddhist meditation can influence healing in ADHD adolescents in relation to peer relationships. Countries, local communities, and private institutions are studying various methods and establishing new organizations to try to solve problems. But It seems difficult to find a fundamental solution. Therefore, this study aims to approach solutions for young people with ADHD through Buddhist meditation from a Buddhist perspective.
 In this article, I first examined the theoretical background of improving peer relationships and Metta meditation, and considered Metta meditation. We also discussed whether there is a possibility of improving peer relationships among young people with ADHD. Metta meditation is a literature review that reveals that emotional composure has the opposite effect of improving interpersonal skills due to excellent coping ability.
 Through this study, it has been revealed that adolescents with ADHD are immature in interaction in peer relationships due to lack of performance in social skills due to lack of attention deficit hyperactivity, and impulsiveness characteristics. Also, adolescents with they have difficulty controlling their emotions and have a tendency to be less responsive to questions than efficiently communicating information. On the other hand, it has been proven that charity meditation stimulates the right brain, activates parasympathetic nerves, increases endorphins in the brain, and is effective in improving peer relationships with positive emotions. Through Metta meditation, ADHD adolescents can look forward to the effect of developing personal resources and helping them resolve conflicts in relationships with peers or people around them by looking at their minds.

МОДЕЛЮВАННЯ НАПРУЖЕНО-ДЕФОРМОВАНОГО СТАНУ МЕТАЛЕВОГО СТРИЖНЕВОГО КАРКАСУ ГЕОДЕЗИЧНОГО КУПОЛУ ДЛЯ РАЦІОНАЛЬНОГО ПРОЕКТУВАННЯ

The paper contains the further developed of method for calculating thin-walled shells with supporting frame in the form of geodesic domes without a stationary foundation. Have been performed the detailed analysis of the fundamental design solutions of frame demountable domes with tent double-layer cover, the inner layer of which serves as a projection screen of three-dimensional cinemas, which are gaining popularity in the amusement industry. Have been developed highly detailed finite element models of dome with a base diameter of 13.5 m, taking into account technological holes and structural elements of rigidity under the influence of wind, snow, ice and other climatic influences. Have been modeled at the same time, various options for connecting the dome frame to the base. Have been proven that the worst influence on the dome structures is the wind influence, based on the stability criterion. Have been proven at also that the frame-rod tented construction of the geodome cannot function safely without reliable connection to the base. Have been identified, areas of the core elements of the frame with the highest internal stresses from various loads for all possible options for connecting the frame to the base. Have been considered the general nature of deformation and possible destruction of the structure, as well as the issue of loss of stability. Have been founded that the most stressed structures include the tent cover and bolted fasteners of the joints of the rod system. Have been proposed a rational method for anchoring frame dome structures at temporary earthen construction sites using geo-screws or metal screw piles. Have been proven the possibility of anchoring the supporting elements of the dome in five polar symmetrical points using ballast. Have been formulated the constructive recommendations regarding the rational design of frame dome systems. Have been developed the technological regulations for the further safe operation of frame geo-domes, and have been outlined the directions for further scientific research on this topic.

Frequency dependent exact trial functions in Galerkin boundary method for free vibration analysis of thin plate

Method of frequency dependent exact trial functions for thin plate vibration based on fundamental solutions of Voigt is suggested. Contrary to other methods, where one of the functions is chosen as the scale and specific boundary condition dependent, it employs only the frequency dependent functions for both space coordinates. Thus they are scale independent, so the same functions can be used for different boundary conditions and plate dimensions. General rule for the choice of exact trial functions is formulated. The boundary conditions are satisfied according to the Galerkin boundary method, which actually minimizes the energy residuals with respect to each weight function (fundamental solution).The verification of method is performed on examples of rectangular plate with various boundary conditions. Several arbitrarily chosen sets of trial functions were employed in calculation of the same tasks, and it is shown that accuracy of the method is almost independent from the choice of them. Even the small number of trial functions provides the very accurate results for natural frequencies.

A fundamental sequences method with time-reduction for one-dimensional lateral Cauchy problems

A fundamental sequences method is derived for the numerical solution of an ill-posed one-dimensional lateral Cauchy problem for a hyperbolic damped wave equation, including as a special case the parabolic heat equation. Either the Laguerre transform or the Houbolt finite difference scheme is applied to reduce the time-dependent lateral Cauchy problem to a sequence of second-order ordinary differential equations (ODEs) with function values and derivatives specified at the right endpoint of a finite space interval. A set of fundamental solutions is constructed, termed a fundamental sequence, to the differential equations. The solution of the obtained ODEs is approximated by a linear combination of elements in the fundamental sequence. Source points are placed outside of the solution interval in space, and by collocating at the endpoints of this interval a sequence of linear equations is obtained for finding the unknown coeficients. Tikhonov regularization is used to render a stable solution to the obtained systems of linear equations. Numerical results both for the parabolic and hyperbolic case confirm the efficiency of the proposed method including noisy data. The presented results complement the higher-dimensional case initiated in our previous researches.