Necessary Conditions for Multistationarity and Stable Periodicity

1998 ◽  
Vol 06 (01) ◽  
pp. 3-9 ◽  
Author(s):  
El Houssine Snoussi
Keyword(s):  
Differential System ◽  
Jacobian Matrix ◽  
Necessary Conditions ◽  
Formal Proof ◽  
Necessary Condition ◽  
Constant Sign ◽  
Interaction Graph ◽  
Partial Derivatives

We show in this paper that, for a differential system defined by a quasi-monotonous function f (with constant sign partial derivatives) the existence of a positive loop in the interaction graph associated to the Jacobian matrix of f is a necessary condition for multistationarity, and the existence of a negative loop comprising at least two elements is a necessary condition for stable periodicity. This gives a formal proof of R.Thomas's conjectures.

Positive and Negative Circuits in Dynamical Systems

1998 ◽  
Vol 06 (01) ◽  
pp. 11-15 ◽  
Author(s):  
Jean-Luc Gouzé
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbit ◽  
Differential System ◽  
Steady States ◽  
Necessary Condition ◽  
Interaction Graph ◽  
Stable Periodic Orbit ◽  
Stable Periodic

We state precisely and demonstrate two conjectures of R. Thomas following which (a) the existence of a positive circuit in the oriented interaction graph of a differential system is a necessary condition for the existence of several steady states, and (b) the existence of a negative non-oriented circuit of length at least two is a necessary condition for the existence of a stable periodic orbit.

scholarly journals On the equivalence of three-dimensional differential systems

2020 ◽  
Vol 18 (1) ◽  
pp. 1164-1172
Author(s):  
Jian Zhou ◽  
Shiyin Zhao
Keyword(s):  
Periodic Solutions ◽  
Differential System ◽  
Necessary Conditions ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Periodic Systems ◽  
Structural Form ◽  
Differential Systems

Abstract In this paper, firstly, we study the structural form of reflective integral for a given system. Then the sufficient conditions are obtained to ensure there exists the reflective integral with these structured form for such system. Secondly, we discuss the necessary conditions for the equivalence of such systems and a general three-dimensional differential system. And then, we apply the obtained results to the study of the behavior of their periodic solutions when such systems are periodic systems in t.

Certain Fourier Transforms of Distributions: II

1954 ◽  
Vol 6 ◽  
pp. 186-189 ◽  
Author(s):  
Eugene Lukacs ◽  
Otto Szász
Keyword(s):  
Characteristic Function ◽  
Fourier Transforms ◽  
Necessary Conditions ◽  
Laplace Transforms ◽  
Characteristic Functions ◽  
Necessary Condition ◽  
Multiple Roots ◽  
Not Given ◽  
Class Of Functions

In an earlier paper (1), published in this journal, a necessary condition was given which the reciprocal of a polynomial without multiple roots must satisfy in order to be a characteristic function. This condition is, however, valid for a wider class of functions since it can be shown (2, theorem 2 and corollary to theorem 3) that it holds for all analytic characteristic functions. The proof given in (1) is elementary and has some methodological interest since it avoids the use of theorems on singularities of Laplace transforms. Moreover the method used in (1) yields some additional necessary conditions which were not given in (1) and which do not seem to follow easily from the properties of analytic characteristic functions.

Eccentricity in irregular multistory buildings

1986 ◽  
Vol 13 (1) ◽  
pp. 46-52 ◽  
Author(s):  
V. W.-T. Cheung ◽  
W. K. Tso
Keyword(s):  
Dynamic Analysis ◽  
Necessary Conditions ◽  
Vertical Axis ◽  
Building Code ◽  
Necessary Condition ◽  
Practical Procedure ◽  
Multistory Buildings ◽  
Plane Frame ◽  
Code Procedure ◽  
Code Provisions

To evaluate the seismic torsional effect on multistory buildings, the concept of eccentricity is extended from single-story buildings to multistory buildings by defining the locations of the centers of rigidity at each floor. A practical procedure to locate the centers of rigidity and hence floor eccentricity is introduced. This procedure depends on the use of plane frame computer programs only and is suitable for use in design offices. The seismic torsional provisions in the National Building Code of Canada 1985 (NBCC 1985) explicitly emphasize that the code provisions apply to buildings where the centres of rigidity lie on a vertical axis only. By means of examples, it verifies the claim of NBCC 1985. Also, it shows that, for buildings with centers of rigidity scattered from a vertical axis, the code procedure may or may not apply. Therefore, one should interpret the condition of centers of rigidity located along a vertical axis to be a sufficient, but not a necessary, condition for the NBCC 85 code provisions to be applicable. Until the necessary conditions are known, dynamic analysis remains the most reliable method to assign the torsional effects to various portions of the building. Key words: building code, center of rigidity, dynamic analysis, eccentricity, irregular, multistory, seismic, torsion.

scholarly journals Syarat Perlu dan Cukup untuk Keterbatasan Potensial Riesz di Ruang Morrey Klasik

2013 ◽  
Vol 14 (3) ◽  
pp. 227
Author(s):  
Mohammad Imam Utoyo ◽  
Basuki Widodo ◽  
Toto Nusantara ◽  
Suhariningsih Suhariningsih
Keyword(s):  
Characteristic Function ◽  
Morrey Space ◽  
Necessary Conditions ◽  
Riesz Potential ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Research Results ◽  
Necessary And Sufficient

This script was aimed to determine the necessary conditions for boundedness of Riesz potential in the classical Morrey space. If these results are combined with previous research results will be obtained the necessary and sufficient condition for boundedness of Riesz potential. This necessary condition is obtained through the use of characteristic function as one member of the classical Morrey space.

scholarly journals PEMENUHAN ELEMEN NECESSARY CONDITIONS KECAMATAN DALAM PENYELENGGARAAN PEMERINTAHAN UMUM DI KABUPATEN PANDEGLANG

2020 ◽  
Vol 4 (2) ◽  
pp. 129-146
Author(s):  
Arif Nugroho ◽  
Delly Maulana
Keyword(s):  
Government Regulation ◽  
Necessary Conditions ◽  
Transitional Period ◽  
Necessary Condition ◽  
Research Approach ◽  
Regional Government ◽  
National Unity ◽  
General Government ◽  
The Government ◽  
Technical Basis

 Artikel ini mengulas Pemenuhan Elemen Necessary Conditions Kecamatan dalam penyelenggaraan pemerintahan umum baik secara nasional dan spesifik diperdalam dengan fakta empiris di Kabupaten Pandeglang, hal itu sebagai konsekuansi dari pelaksanaan Undang – Undang Nomor 23 Tahun 2014. Penelitian dilakukan dengan menggunakan pendekatan kualitatif. Hasil penelitian diketahui, penyelenggaraan pemerintahan umum Kecamatan baik fakta secara nasional serta pendalaman fakta empiris di Kabupaten Pandeglang menunjukan belum cukup tertopang oleh elemen necessary condition diantaranya kepastian atas kewenangan legalnya serta anggaran yang menyertainya. Oleh sebab itu dipandang perlu ada kemauan politik baik itu dari Presiden untuk segera mengundangkan Peraturan – Pemerintah sebagai landasan teknis bagi pemerintah daerah selaku kepala wilayah maupun dari Kepala Daerah Kabupaten/Kota untuk melakukan terobosan agar supaya di masa peralihan implementasi Undang – Undang Nomor 23 Tahun 2014 kewenangan – kewenangan pada bidang kesatuan bangsa, keamanan dan keteriban umum dapat dilimpahkan pada Kecamatan serta Elemen Necessary Conditions lain yang menyertainya diperkuat.     This article discusses the fulfillment of the elements of the sub-district's necessary conditions in the administration of general government both nationally and specifically and deepened by empirical facts in Pandeglang Regency, this is a consequence of the implementation of Law Number 23 of 2014. The research approach used is qualitative. The results showed that in the administration of district general government both the facts nationally and the deepening of empirical facts in Pandeglang district were not sufficiently supported by elements of necessary conditions, including certainty of legal authority and budget. Therefore, there needs to be political will, both from the president, to immediately ratify the Government Regulation as a technical basis for the regional government (Territory) as well as from the Head of Regency / City to make breakthroughs so that in the transitional period the implementation of Law Number 23 Year 2014 powers in the areas of national unity, security and public order can be transferred to the District and the accompanying elements of necessary conditions are strengthened.

Optimal Trajectories and the Accessory Minimum Problem

1965 ◽  
Vol 16 (3) ◽  
pp. 205-220 ◽  
Author(s):  
D. J. Bell
Keyword(s):  
Necessary Conditions ◽  
Sounding Rocket ◽  
Necessary Condition ◽  
Minimum Problem ◽  
Multiplier Rule ◽  
Variation Of A Function ◽  
Accessory Minimum Problem ◽  
The First Variation ◽  
The Second Variation

SummaryThe necessary conditions of Clebsch and Weierstrass and of the multiplier rule in the calculus of variations, which arise from the study of the first variation of a function, are summarised. A further necessary condition associated with the second variation is stated. The latter condition is applied to two problems: (i) the determination of the thrust-time programme which maximises the altitude of a sounding rocket, (ii) the determination of the thrust direction programme for a rocket with a known propellant expenditure programme which yields a maximum range. In both problems it is found that the additional necessary condition is satisfied.

scholarly journals An Accurate Jacobian Matrix with Exact Zoeppritz for Elastic Moduli of Dry Rock

2019 ◽  
Vol 9 (24) ◽  
pp. 5485
Author(s):  
Xiaobo Liu ◽  
Jingyi Chen ◽  
Fuping Liu ◽  
Zhencong Zhao
Keyword(s):  
Jacobian Matrix ◽  
Incidence Angle ◽  
Inversion Method ◽  
Seismic Velocities ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Shear Moduli ◽  
Partial Derivatives ◽  
Solid Matrices ◽  
Derivatives Of

Seismic velocities are related to the solid matrices and the pore fluids. The bulk and shear moduli of dry rock are the primary parameters to characterize solid matrices. Amplitude variation with offset (AVO) or amplitude variation with incidence angle (AVA) is the most used inversion method to discriminate lithology in hydrocarbon reservoirs. The bulk and shear moduli of dry rock, however, cannot be inverted directly using seismic data and the conventional AVO/AVA inversions. The most important step to accurately invert these dry rock parameters is to derive the Jacobian matrix. The combination of exact Zoeppritz and Biot–Gassmann equations makes it possible to directly calculate the partial derivatives of seismic reflectivities (PP-and PS-waves) with respect to dry rock moduli. During this research, we successfully derive the accurate partial derivatives of the exact Zoeppritz equations with respect to bulk and shear moduli of dry rock. The characteristics of these partial derivatives are investigated in the numerical examples. Additionally, we compare the partial derivatives using this proposed algorithm with the classical Shuey and Aki–Richards approximations. The results show that this derived Jacobian matrix is more accurate and versatile. It can be used further in the conventional AVO/AVA inversions to invert bulk and shear moduli of dry rock directly.

scholarly journals Formal Weierstrass Nonintegrability Criterion for Some Classes of Polynomial Differential Systems in ℂ2

2020 ◽  
Vol 30 (04) ◽  
pp. 2050064
Author(s):  
Jaume Giné ◽  
Jaume Llibre
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Differential System ◽  
Integrable Systems ◽  
Necessary Conditions ◽  
Differential Systems ◽  
Polynomial Differential Systems ◽  
Formal Power

In this paper, we present a criterion for determining the formal Weierstrass nonintegrability of some polynomial differential systems in the plane [Formula: see text]. The criterion uses solutions of the form [Formula: see text] of the differential system in the plane and their associated cofactors, where [Formula: see text] is a formal power series. In particular, the criterion provides the necessary conditions in order that some polynomial differential systems in [Formula: see text] would be formal Weierstrass integrable. Inside this class there exist non-Liouvillian integrable systems. Finally we extend the theory of formal Weierstrass integrability to Puiseux Weierstrass integrability.

On the Elusiveness of ββ0ν Decay

1998 ◽  
Vol 07 (03) ◽  
pp. 405-418
Author(s):  
Tsan Ung Chan
Keyword(s):  
Neutral Particle ◽  
Necessary Conditions ◽  
Lepton Number ◽  
Necessary Condition ◽  
Experimental Fact ◽  
Neutral Particles ◽  
Zero Mass ◽  
Number Conservation

To date, no evidence of ββ0ν decay has been found despite tremendous experimental efforts. In contrast, ββ2ν decay has been clearly and definitely observed in several nuclei. These experimental facts question the reality of ββ0ν decay. This ββ0ν decay which violates lepton number conservation can only occur if the neutrino is massive and is its own antiparticle or in other words is a truly neutral particle. The observation of this decay implies then that the neutrino is a truly neutral particle and it has a non-zero mass. But the absence of ββ0ν decay implies only that at least one of the two necessary conditions is not fulfilled. Since the truly neutral character of neutrino is a necessary condition, it is important to provide objective criteria of truly neutral particles. We propose a generalized Gell-Mann and Nishijima formula which provides naturally the criteria of truly neutral particles. According to these criteria n and ν are different from their antiparticles for symmetric reason. The absence of ββ0ν decay could then be simply understood. Indeed a truly neutral particle could be more generally defined as a neutral particle with respect to all charges and is its own antiparticle. The Dirac character of the neutrino does not contradict any experimental fact.

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