Second-order Lagrangians admitting a first-order Hamiltonian formalism

Let p: E —» JV be an arbitrary fibred manifold over a connected n-dimensional manifold N oriented by a volume form v = dx1^-...^dxn, and let pk: JkE → N be the bundle of K-jets of local sections of p, with projections Plk : JkE → JlE for every k ≥ 1

Registrum in sermones Jacobi de voragine de tempore.

Hojas imp. por ambas caras

Aureum opus regalium priuilegiorum ciuitatis et regni Valentie : cum historia cristianissimi Regis Jacobi ...

Texto en latin y valenciano

A formalism and method for representing and reasoning with process models authored by subject matter experts

Enabling Subject Matter Experts (SMEs) to formulate knowledge without the intervention of Knowledge Engineers (KEs) requires providing SMEs with methods and tools that abstract the underlying knowledge representation and allow them to focus on modeling activities. Bridging the gap between SME-authored models and their representation is challenging, especially in the case of complex knowledge types like processes, where aspects like frame management, data, and control flow need to be addressed. In this paper, we describe how SME-authored process models can be provided with an operational semantics and grounded in a knowledge representation language like F-logic in order to support process-related reasoning. The main results of this work include a formalism for process representation and a mechanism for automatically translating process diagrams into executable code following such formalism. From all the process models authored by SMEs during evaluation 82% were well-formed, all of which executed correctly. Additionally, the two optimizations applied to the code generation mechanism produced a performance improvement at reasoning time of 25% and 30% with respect to the base case, respectively.

D. Jacobi Parez de Valêtia... In centû & quinquagita [sic] psalmos Dauidico quos oês a Dauid prophetice côpositos ad illustratione fidei nostrae conuincit...

Fecha en colofón

D. Jacobi Parez [sic] de Vale[n]tia ... ordinis diui Augustini ... expositiones in. CL. psal. Dauidicos ... Cantica ferialia in biblijs contenta. Cantica eua[n]gelica B[e]n[e]dictus Magnificat nu[n]c dimit. Gl[or]ia in excel. Ca[n]ticu[m] Amb. et Aug. Te Deum. Cantica canticor[um] Premissis Questio[n]ib[us] et earu[m] subtilissimis resolutionibus co[n]tra Judeos nostre fidei adversa [Texto impreso] : Cum tabula in totu[m] opus collecta

Marca tip. en port. y colofón en h. [27]

Integrability of second-order Lagrangians admitting a first-order Hamiltonian formalism

Second-order Lagrangian densities admitting a first-order Hamiltonian formalism are studied; namely, i) necessary and sufficient conditions for the Poincaré–Cartan form of a second-order Lagrangian on an arbitrary fibred manifold p : E → N to be projectable onto J 1 E are explicitly determined; ii) for each of such Lagrangians, a first-order Hamiltonian formalism is developed and a new notion of regularity is introduced; iii) the variational problems of this class defined by regular Lagrangians areprovedtobeinvolutive

1.3 Charles Hamilton Houston, NAACP Chief Attorney, 1930-54

The NAACP’s legal team, which eventually included Thurgood Marshall, had a strategy in mind for confronting the Plessy v Ferguson “separate but equal” Supreme Court decision of 1896. Walter White, the NAACP President assisted Houston in developing the plan. By concentrating on the “equal” aspect of Plessy, the NAACP would attempt to make “separate but equal” a financial impossibility for states toeing the line of “Jim Crow” laws. In the words of Charles Hamilton Houston, “we are going to bleed them white.”

New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

Os artigos federalistas : a contribuição de James Madison, Alexander Hamilton e John Jay para o surgimento do Federalismo no Brasil

Inclui bibliografia.

Plea in the case of Hamilton v. Saunders, 1763

Plea in response to the plaintiff's declaration. Signed: (Charles) Pinckney, defendant's attorney, and John Rutledge (plaintiff's attorney?). Note on verso: Filed 4th May 1763.