Derivation of the Fixed-Points Theory with Some Numerical Simulations for Global Vibration Control of Structure with Closely Spaced Natural Frequencies

Dayou, Jedol,Wang, Semyung Marcel Dekker inc. 2006 MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES Vol.34 No.1

<P> The fixed-points theory has been used as one of the design laws in fabricating a vibration neutralizer for the control of a relatively simple structure. The underlying principle of the theory is that in the frequency response function (FRF) of the system considered, there exist two fixed points that are common to all FRF curves regardless of the damping value of the neutralizer. It is possible, with the proper selection of the neutralizer's resonance frequency, to determine the optimal damping value of the neutralizer that provides a smooth FRF by following the standard procedure of the theory. Recently, the authors have extended the application of the theory for global vibration control of a continuous structure with well separated natural frequencies. In this paper, the application is further extended to global vibration control of a structure with natural frequencies that are closely spaced. Through some numerical simulations, it is shown that the theory can also be used to remove the effects of the dominant mode within the frequency range where the global response is dominated by that mode. However, there are some limitations in its application especially for the overlapping natural frequencies.</P>

$(\alpha, \beta)$-intuitionistic fuzzy fixed point theory for $(\alpha, \beta)$-intuitionistic fuzzy monotone multifunctions

Abdelkader Stouti 원광대학교 기초자연과학연구소 2017 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.14 No.2

In this paper, we first introduce the notion of (α, β)-intuitionistic fuzzy order relation for any two positive reals numbers α and β such that (α, β) ∈]0, 1] × [0, 1[ with α + β ≤ 1. Secondly, we prove the existence of a maximal and a minimal (α, β)-intuitionistic fuzzy fixed points. Also, we establish the existence of the greatest and the least (α, β)-intuitionistic fuzzy fixed points. Furthermore, we give an (α, β)-intuitionistic fuzzy version of Tarski’s fixed point Theorem.

Optimization of response of a dynamic vibration absorber forming part of the main system by the Fixed-point theory

Houshyar Eimani Kalehsar,Nahmat Khodaie 대한토목학회 2018 KSCE JOURNAL OF CIVIL ENGINEERING Vol.22 No.7

In the classic form of the Dynamic Vibration Absorber (DVA), a damped DVA is attached to an undamped primary mass, and themain tuning objective is to minimize the dynamic response of the primary mass. Recently proposed structural systems with the selfcontrolability such as controlled mega-substructure and core tubes with suspension systems use part of the main structure as adynamic vibration absorber. Because the DVA in the self-control structural systems is a part of the main structure, the controlobjective of these kinds of systems is dual not only to limit the motion of the primary system but also to reduce the vibration of theDVA. In the present study, the simplified classic model of the DVA with the primary mass under the harmonic excitation is studiedand the fixed-point theory is used to derive the optimum parameters of the DVA to minimize the maximum displacement andacceleration responses of the DVA. The effects of different design parameters such as the mass and stiffness ratios of the DVA on theresponse of the system are investigated. It is shown that the coordinates of one of the fixed points in both displacement andacceleration responses of the DVA are independent of the natural frequency and damping ratios. This point plays an important role inthe optimization procedure. For a specific range of the mass ratios of the DVA, the maximum response of the DVA is larger than thatof the primary mass; therefore, optimization based on the response of the DVA yields a better result for the self-control structuralsystem.

EXISTENCE AND STABILITY RESULTS OF GENERALIZED FRACTIONAL INTEGRODIFFERENTIAL EQUATIONS

C. Kausika,K. Balachandran,N. Annapoorani,J. K. Kim 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.4

This paper gives sufficient conditions to ensure the existence and stability of solutions for generalized nonlinear fractional integrodifferential equations of order $\alpha$ ($1 < \alpha < 2$). The main theorem asserts the stability results in a weighted Banach space, employing the Krasnoselskii's fixed point technique and the existence of at least one mild solution satisfying the asymptotic stability condition. Two examples are provided to illustrate the theory.

Existence results for impulsive neutral functional integrodifferential equations with infinite delay

Park, J.Y.,Balachandran, K.,Annapoorani, N. Pergamon Press 2009 Nonlinear analysis Vol.71 No.7

This paper is concerned with the existence of mild solutions for impulsive neutral functional integrodifferential equations with infinite delay in Banach spaces. The results are obtained by using the Krasnoselski-Schaefer type fixed point theorem. An example is provided to illustrate the theory.

Boundary controllability of Semilinear Systems in Banach spaces

BALACHANDRAN, K.,ANANDHI, E.R. 한국산업정보응용수학회 2001 한국산업정보응용수학회 Vol.5 No.2

Sufficient conditions for boundary controllability of semilinear systems in Banach spaces are established. The results are obtained by using the analytic semigroup theory and the Banach contraction principle. An example is provided to illustrate the theory.

복지포인트의 임금성 및 통상임금성 인정 여부

최정은 사법발전재단 2020 사법 Vol.1 No.51

판례는 근로자가 자신의 노동력을 사용자의 지휘·처분하에 두고 제공한 근로에 대한 대가로서 근로자에게 계속적·정기적으로 지급되고, 단체협약, 취업규칙, 근로계약, 노동관행 등에 의해 사용자에게 지급의무가 있으면 임금에 해당한다고 판시해 오고 있다. 한편 판례는 실비변상적 금원, 1회성으로 지급하는 금품 또는 은혜적으로 지급한 금품의 임금성을 부정한다. 나아가 대법원 1995. 12. 21. 선고 94다26721 전원합의체 판결로 임금 이분설이 폐기된 이래 판례는 복리후생적 금품이 근로기준법상 임금 즉 ‘근로의 대가’에 해당하는지에 대하여 위와 같은 일반적인 임금성 판단 기준을 동일하게 적용하는 것으로 이해된다. 판례 중에는 가족수당, 일비, 음료대, 식대, 명절 선물의 임금성을 인정한 사례들이 있는 반면에, 자녀 학비보조비, 사택 제공, 식대의 임금성을 부정한 사례들도 보인다. 복지포인트는 비교적 최근에 기업복지의 일환으로 도입된 선택적 복지제도에 따라 많은 사업장에서 근로자에게 부여해 온 것으로, 물품과 서비스를 구매하는 온라인 결제수단으로도 기능하고 있다. 선택적 복지제도는 미국의 카페테리아 플랜이 1990년대 말 우리나라에 도입되어 그로부터 10여 년 사이에 일반 사기업은 물론 공기업과 공공기관, 지방자치단체 등으로 빠르게 확산 및 정착된 것으로, 제도의 설계, 운영 등에 관하여는 근로복지기본법에 근거를 두고 있다. 그런데 선택적 복지제도에 따른 복지포인트는 사용자가 단체협약이나 취업규칙 등에 지급에 관한 근거를 두고 계속적·정기적으로 모든 근로자에게 지급한다는 점에서 근로기준법상 임금 즉 근로의 대가로 볼 수 있고 정기적·고정적·일률적으로 지급되는 통상임금에도 해당되는지에 관한 논란이 여러 임금 소송에서 제기되었고, 이에 관한 하급심 판결례는 복지포인트의 임금성 및 통상임금성을 긍정한 판결례와 부정한 판결례로 나뉘어져 있었다. 대상판결은 복지포인트의 임금성 및 이를 전제로 한 통상임금성에 관한 그간의 논란을 전원합의체 판결로 정리하였다. 다수의견은 근로복지의 개념에서 임금 등 근로조건을 제외하고 있는 근로복지기본법 규정, 선택적 복지제도의 연혁과 도입 경위, 운영 목적 등에 비추어 근로의 대가라기보다는 새로운 형식의 기업복지제도의 설정이라는 측면을 중시하여 복지포인트의 임금성을 부정하였다. 복지포인트의 사용 용도가 제한되어 있고 통상 1년의 사용기간이 지나면 소멸하며 근로제공과 무관하게 매년 초에 일괄하여 배정되는 복지포인트의 특성, 임금 지급 원칙과의 부조화 등이 고려되었고, 임금으로 보호할 필요성에 관한 목적론적 관점도 가미되었다. 이에 대하여는, 복리후생적 성격이 임금성을 부정할 수 있는 근거가 될 수 없고, 선택적 복지제도는 종래 존재하던 임금의 성격을 가지는 각종 복지수당을 통합한 것에 불과하며, 복지포인트의 배정 자체가 통화 지급과 실질적으로 다르지 않다는 데에 중점을 두고 복지포인트의 임금성 및 통상임금성을 긍정하는 입장(반대의견)과 복지포인트의 임금성을 긍정하되 통상임금성을 부정하는 입장(별개의견)에서 상세한 반론이 제기되었다. 대상판결에 따르면 적어도 사용자가 직접 운영하는 선택적 복지제도에 기반을 두고 근로자에게 부여하는 복지포인트에 관하여는 임금성을 인정하기 어렵다. 비임금성 복지제도로서 선택적 복지 ... Precedents have concluded that any reward given on a continual and regular basis as remuneration for work provided by an employee, who put his or her labor power under supervision and guidance of an employer having the obligation of payment pursuant to collective agreements, employment regulations, employment agreements and labor practices, constitutes a wage. Meanwhile, precedents have denied that (i) money and valuables to reimburse actual costs, (ii) one-off money and valuables, and (iii) money and valuables for beneficence cannot be deemed to have the attributes of wage. Since Supreme Court en banc Decision 94Da26721 Decided December 21, 1995 discarded the theory of wage dichotomy, precedents are understood to have equally applied a general standard of determining whether any reward has the attributes of wage in determining whether money and valuables given out as welfare benefits constitute a wage, or, what is stated as “remuneration for work” under the Labor Standards Act. Precedents include cases holding that family allowances, daily expenses, food and drink expenses, and holiday gifts can be deemed as having the attributes of wage, and cases dismissing school fee subsidies for employee’s children, provision of company housing and meal expenses cannot be deemed as having the attributes of wage. Welfare points have been provided to employees in a number of workplaces in accordance with the selective welfare system that was introduced not so long ago as part of a corporate welfare scheme, and are used as online payment methods to purchase goods and services. First introduced at the end of 1990s and dubbed as the Korean version of the cafeteria plan in the United States, the selective welfare system was quickly disseminated to and established in not only private businesses but also state-owned companies, public agencies and local governments over the course of 10 years, and is based on the Framework Act on Labor Welfare with respect to the design and management of the scheme. Considering that welfare points offered under the selective welfare system are offered to all employees on a continual and regular basis pursuant to collective agreements or employment regulations, they can be considered as constituting a wage, or, in other words, remuneration for work. Many wage-related lawsuits have been filed with respect to disputes over determining whether these welfare points can be deemed as ordinary wages paid on a regular, fixed and consistent basis. Lower court decisions on this matter were categorized into those that acknowledged the attributes of wage and ordinary wage with respect to welfare points, and those that did not. The subject case summed up persistent disputes over the attributes of wage and ordinary wage with respect to welfare points in an en banc decision. The Majority Opinion denied that welfare points had the attributes of wage by underlining the aspect of a new form of corporate welfare scheme rather than viewing it as remuneration for work, in light of the provisions of the Framework Act on Labor Welfare that excludes working conditions, such as wage, from the concept of labor welfare, the chronology and background leading up to the introduction of the selective welfare system, and the purpose of the system. It took account of the characteristics of welfare points, including (i) limited use of welfare points, (ii) that they cease to exist after a one-year period, and (iii) that welfare points are allocated in a lump sum at the beginning of every year irrespective of provision of labor, the inconsistency with the principles of wage payment, and purpose-oriented perspective centered around the need for its protection as a wage. As for these points of arguments, the Dissenting Opinion affirmed that welfare points can be considered as having the attributes of wage and ordinary wage by arguing that: (i) deeming that welfare points cannot be considered as having the attributes of wage on grounds of ...

Fixed point theory in Fr´echet spaces for M¨onch inward and contractive Urysohn type operators

Donal O'Regan 영남수학회 2008 East Asian mathematical journal Vol.24 No.3

We present new fixed point theorems for inward and weakly inward Urysohn type maps. Also we discuss M¨onch Kakutani and contractive type maps.

FIXED POINT THEORY IN $FR{\acute{E}}CHET$ SPACES FOR $M{\ddot{O}}NCH$ INWARD AND CONTRACTIVE URYSOHN TYPE OPERATORS

O'Regan, Donal The Youngnam Mathematical Society Korea 2008 East Asian mathematical journal Vol.24 No.3

We present new fixed point theorems for inward and weakly inward Urysohn type maps. Also we discuss $M{\ddot{o}}nch$ Kakutani and contractive type maps.

FIXED POINT THEORY FOR VARIOUS CLASSES OF PERMISSIBLE MAPS VIA INDEX THEORY

Agarwal, Ravi P.,O'Regan, Donal Korean Mathematical Society 2009 대한수학회논문집 Vol.24 No.2

In this paper we use degree and index theory to present new applicable fixed point theory for permissible maps.