The sum-product algorithm is a well-known procedure for marginalizing an "acyclic'' product function whose range is the ground set of a commutative semiring. The algorithm is general enough to include as special cases several classical algorithms developed in information theory and probability theory. We present four results. First, using the sum-product algorithm we show that the variable sets involved in an acyclic factorization satisfy a relation that is a natural generalization of probability-theoretic independence. Second, we show that for the Boolean semiring the sum-product algorithm reduces to a classical algorithm of database theory. Third, we present some methods to reduce the amount of computation required by the sum-product algorithm. Fourth, we show that with a slight modification the sum-product algorithm can be used to evaluate a general sum-product expression.
The purpose of this aer is to define the nature, history, and scope of the Surealist movement in Egypt in the 1930s and the 1940s and its influence on contemporary Egyptian art. It is also desigend to provide a clear, accessible, and broad background on a diverse group of mainstream and lesser-known innovativde Arabic artists while showing that Surrealism is not a phenomenon unique to Europe. In addition to dealing with the general state of the Egyptian art scene in the 1930s, the aarticle covers the genesis of the Egyptian Surrealis group Art and Liberty and its exhibitions, political activities and two main members, Georges Hénein and Ramsīs Yūnān.
A definition of “Šipoš integral” is given, similarly to [3],[5],[10], for real-valued functions and with respect to Dedekind complete Riesz-space-valued “capacities”. A comparison of Choquet and Šipoš-type integrals is given, and some fundamental properties and some convergence theorems for the Šipoš integral are proved.
The annual oscillations of the brightnesses observed at 12 and 25 μm by IRAS near the ecliptic poles are mainly due to the inclination of the symmetry plane (SP) of the interplanetary dust cloud upon the ecliptic, but also, secondarily, to the eccentricity of the earth's orbit.
Comparing the brightnesses at the poles and in the ecliptic (near 90° elongation) allows a retrieval of the inclination i and ascending node Ω SP/ecliptic through an inversion technique, with very little model-dependence. The results (i = 1.5°, Ω = 90°) conflict with some of those previously obtained from the same observations by more model-dependent approaches, but they agree with former optical determinations from D2A satellite and from Tenerife
ground-based data.
The Routh reduction of cyclic variables in the Lagrange function and the Jacobi-Maupertuis principle of constant energy systems are generalized. The article deals with one-dimensional variational integral subject to differential constraints, the Lagrange variational problem, that admits the Lie group of symmetries. Reduction to the orbit space is investigated in the absolute sense relieved of all accidental structures. In particular, the widest possible coordinate-free approach to the underdetermined systems of ordinary differential equations, Poincaré-Cartan forms, variations and extremals is involved for the preparation of the main task. The self-contained exposition differs from the common actual theories and rests only on the most fundamental tools of classical mathematical analysis, however, they are applied in infinite-dimensional spaces. The article may be of a certain interest for nonspecialists since all concepts of the calculus of variations undergo a deep reconstruction.
Some open problems appearing in the primary article on the symmetry reduction are solved. A new and quite simple coordinate-free definition of Poincaré-Cartan forms and the substance of divergence symmetries (quasisymmetries) are clarified. The unbeliavable uniqueness and therefore the global existence of Poincaré-Cartan forms without any uncertain multipliers for the Lagrange variational problems are worth extra mentioning.
Like the classical Gram-Schmidt theorem for symplectic vector spaces, the sheaf-theoretic version (in which the coefficient algebra sheaf $\mathcal A$ is appropriately chosen) shows that symplectic $\mathcal A$-morphisms on free $\mathcal A$-modules of finite rank, defined on a topological space $X$, induce canonical bases (Theorem 1.1), called symplectic bases. Moreover (Theorem 2.1), if $(\mathcal {E}, \phi )$ is an $\mathcal A$-module (with respect to a $\mathbb C$-algebra sheaf $\mathcal A$ without zero divisors) equipped with an orthosymmetric $\mathcal A$-morphism, we show, like in the classical situation, that “componentwise” $\phi $ is either symmetric (the (local) geometry is orthogonal) or skew-symmetric (the (local) geometry is symplectic). Theorem 2.1 reduces to the classical case for any free $\mathcal A$-module of finite rank.
For companies doing business in mining mineral deposits, ensuring safe work is one of the key tasks (Safety First!). One of the important trends in this area is prevention and endeavour to forestall risk situations. Risks need to be searched, technically described, spatially defined, evaluated and categorized by degree of risk. Complex geological and stability conditions can be one of the sources of persistent and significant risks, which are mainly landslides and rockslides threatening both mining equipment and employees. The problem described in this article and its solution concerns the Most Basin (formerly the North Bohemian Lignite Basin). This is a tertiary basin that was founded in the Oligocene. The main mineral is lignite and mining takes place on the surface. The main excavating machinery in the surface lignite quarries in Europe (Czech Republic, Germany, Poland) is the bucket wheel excavator., Roman Kapica, Dana Vrublová and Martin Vrubel., and Obsahuje bibliografii
The Tachyusa coarctata species group is revised. The species group is defined on the basis of the distinctly asperate punctation on elytra, the dense punctation on tergites III-V with interstices between punctures 1.5-2.0 times their diameter, and the dense, subrecumbent pubescence on the abdomen. The T. coarctata species group is composed of twenty three species restricted in occurrence to the Holarctic and Africa, including one new species described from Iran: Tachyusa frischi sp.n. A revised key to the species in this group is provided. An analysis of the phylogeny of the Tachyusa coarctata species group based on cladistic methods is presented and the phylogenetic relationships among species are discussed.
About 200 observations from AD66 to 1910 of the tail length of Comet Halley have been used to derive the mean tail length of the comet as visible to the naked eye under very good observing conditions, The curve, covering an interval of -45-^ (t-T)^ 80 days, is skewed and peaks at -SS million km for (t-T) secular decrease of the tail length.