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This paper concerns the general characteristics of the Academy of Arts and Sciences in Cracow and the Memoirs of the Academy of Arts and Sciences in Cracow. Moreover, in the context of the global development of the theory of differential equations we present in this paper the articles of Alojzy Jan Stodółkiewicz (1856-1934), Władysław Zajączkowski (1837-1898), Jan Rajewski (1857-1906), Wawrzyniec Żmurko (1824-1889) and Edward Władysław Skiba (1843-1911) on differential equations, which were published in the Memoirs of the Academy of Arts and Sciences in Cracow.

This paper concerns the general characteristics of the Natural Science Society in Paris and the Memoirs of the Natural Science Society in Paris. Moreover, in the context of the development of the theory of differential equations in the world, we present in this paper the articles of Y. Villarceau (1813), W. Zajączkowski (1837–1898) and W. Folkierski (1842–1904) on differential equations, which were published in Memoirs of the Natural Science Society in Paris.

The paper will investigate the possibility of the formation of a speculative bubble in the U.S. stock markets after the 2007-2008 crises. The work is initiated by the observation of historically high equity prices in the stock markets as pointed out by Professor Robert J. Shiller in his new edition of his book ‘Irrational Exuberance’. Until recently the development of a methodology which can be used to detect bubble in real time has been challenging and previous work has mainly focused on ex-post econometric tests in time series that contain only one bubble. The paper uses the recent methodology developed by Philips et. al. that fixes for these deficiencies and enable real time monitoring of statistically significant exuberance and multiple collapsing bubbles within a single time series. Both NASDAQ and S&P 500 indexes are considered and investigation regarding exuberance that cannot be explained by the market fundamentals is conducted.

In this paper, we present a methodological proposal of the design of an SRP, based on the paradigm of questioning the world and inspired by the methodology for the design of didactic activities based on mathematical modeling Consuelo Macias (2012). The analysis of a course of automatic control turns out to be a key element to determine the generatrix question that motivates the SRP. The analysis a priori shows the form in which the students might develop three stages of SRP and to use the differential equations to control the speed of an engine of direct current. The methodological proposal for the design of an SRP, it is considered to be useful for the vocational training. [ABSTRACT FROM AUTHOR]

Abstract: A theorem of Obata states that a complete Riemannian manifold of dimension admitting a nontrivial function f satisfying the differential equation is a sphere (Obata, 1962). In this paper, we propose to study the analogous situation for some Riemannian foliations of dimension 1 or codimension 1 on Riemannian manifolds of dimension . [Copyright &y& Elsevier]

This paper is intented to study both free and forced vibration of a nonlinear structure with cyclic symmetry, under geometric nonlinearity, through use of the harmonic balance method (HBM). In order to study the influence of nonlinearity due to the large deflection of blades, a simplified model has been developed. After adjusting the model parameters, this approach leads to a system of linearly-coupled, second-order nonlinear differential equations, in which nonlinearity appears via quadratic and cubic terms. Periodic solutions, are sought by applying HBM coupled with an arc length continuation method. En the free case, in addition to featuring similar and nonsimilar nonlinear modes, the unforced system is shown to contain localized nonlinear modes. In the forced case, several cases of excitation have been analyzed (low-engine-order excitation and detuned excitation) and we study the influence of the excitation level on the structure of dynamical response. For a sufficiently-detuned excitation, we show that several solutions can coexist, some of them being represented by closed curves in the frequency-amplitude domain. [ABSTRACT FROM AUTHOR]

In this paper we give a numerical method for the study of the decay of the energy of a network of strings. This method is based on a theoretical and numerical construction of some operator say of type τ by the D'Alembert formula. Moreover we give some illustrations of this method. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we prove that every entire curve in a smooth hypersurface of degree in must satisfy an algebraic differential equation of order 3. The logarithmic version of this result is given proving that every entire curve in the complement of a smooth surface of degree in must satisfy an algebraic differential equation of order 3. [Copyright &y& Elsevier]

Abstract: In this paper we will study some questions concerning solutions of Yamabe''s equation on an annulus of with different data on the boundary. The important problem: “what about the radial solution u satisfying () and ” is solved. [Copyright &y& Elsevier]

Abstract: The paper is concerned with a surface evolution problem in the cylindrical case. The physical configuration consists in an axisymmetric stressed pore channel as described in [J. Colin, J. Grilhé, N. Junqua, Morphological instabilities of a stressed pore channel, Acta Mater. 45 (9) (1997) 3835–3841]. When axial stress is applied, morphological instabilities may appear at the vacuum/material interface. Under the axial symmetry envisaged, the radius of the pore channel satisfies a nonlinear evolution equation. Under some formal asymptotic assumptions as in [M. Boutat, Y. D''Angelo, S. Hilout, V. Lods, Existence and finite-time blow-up for the solution to a thin-film surface evolution problem, Asymptotic Anal. 38 (2) (2004) 93–128], we obtain a parabolic 4th-order PDE. Local existence and uniqueness of the solution is established and numerical results showing either a dissipative behaviour or a pinch-off of the solution (depending on initial condition and value of the parameter η) are obtained. To cite this article: M. Boutat et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005). [Copyright &y& Elsevier]

Abstract: Let Ω be an opened domain of with a boundary Γ. The problem numbered (1) in the text has a unique solution in , if , on a part of Γ the area S of which is different from zero and . ɛ is the damping of an elastic structure and ζ is the normalised acoustic impedance of the internal wall of the cavity. ɛ and are small parameters. Thanks to a proper modal expansion and a mean over a narrow band of wave number k, an integral relation between the trace of u on and g is built to the first order in and ɛ, using the residues theorem. It is not an equivalent equation to the problem, but just a step towards its resolution, which will be published in future papers. To cite this article: D. Brenot, C. R. Acad. Sci. Paris, Ser. I 340 (2005). [Copyright &y& Elsevier]

Abstract: Let T be a closed positive current of dimension p in and H an analytic subvariety of of dimension . We denote by the slice of T in H if it exists. We consider the functions on defined by and . The aim of this paper is to establish relationship between the growth of these functions. We prove results generalizing those of L. Gruman in [Séminaire Lelong–Skoda 1981–1983, Lecture Notes in Math., vol. 1028, Springer-Verlag, Berlin, 1983, pp. 125–162] and B. Molzan, B. Shiffman and N. Sibony in [Math. Ann. 257 (1981) 43]. [Copyright &y& Elsevier]

This paper is concerned with incompressible viscoelastic fluids which obey a differential constitutive law of White–Metzner type. We establish the existence and uniqueness of local solutions in 3-D as well as the global existence of small solutions. We then deduce the existence and asymptotic stability of small periodic and stationary solutions. Finally, we prove that the 2-D results obtained in Hakim (J. Math. Anal. Appl. 185 (1994) 675–705) remain true without any restriction on the smallness of the retardation parameter which is the linking coefficient between the equation of velocity (Navier–Stokes equation) and the transport equation verified by the extra-stress tensor. To cite this article: L. Molinet, R. Talhouk, C. R. Acad. Sci. Paris, Ser. I 338 (2004). [Copyright &y& Elsevier]

In this paper we prove a global well-posedness result for the following Cauchy problem: ∂ttu−Δu+a0∂tu+∑lower limit i=1, upper limit 3 ai∂xiu+Vu=−u&z.sfnc;u&z.sfnc;α−1, for (t,x)∈Rt×R3x, u(0)=f, ∂tu(0)=g, where the initial data (f,g)∈H˙1(R3)×L2(R3) are compactly supported, 1&les;α<5, ai(t,x)∈L∞(Rt×Rx3), V(t,x)∈L∞(Rt;L3(R3x)). To cite this article: N. Visciglia, C. R. Acad. Sci. Paris, Ser. I 338 (2004). [Copyright &y& Elsevier]