The essentially Σ1 formulae of ΣL are exactly those which are provably equivalent to a disjunction of conjunctions of 2 and Σ1 formulae.

We characterize the compactness of commutators in Bloom setting. Namely, for a suitably non-degenerate Calderón–Zygmund operator T, and pair weights σ , ω ∈ A p commutator [ T b ] is compact from L ( ) → if only V M O ν where = / 1 . This extends work first author, Holmes Wick. The weighted VMO spaces are different classical space. In dimension d compactly supported smooth functions dense but t...

We consider weighted Reed-Muller codes over point ensemble S1 × · · · × Sm where Si needs not be of the same size as Sj . For m = 2 we determine optimal weights and analyze in detail what is the impact of the ratio |S1|/|S2| on the minimum distance. In conclusion the weighted Reed-Muller code construction is much better than its reputation. For a class of affine variety codes that contains the ...

The most popular algorithms for generation of minimal spanning tree are Kruskal’s[2] and Prim’s[2] algorithm. Many algorithms have been proposed for generation of all spanning tree. This paper deals with generation of all possible spanning trees in increasing cost of a weighted graph. This approach uses one matrix called Difference Weighted Circuit Matrix (DWCM); it is little bit modification o...

OBJECTIVE To explore experimental RBCs derived from a successful commercially available RBC (Grandio) to investigate resin monomer blend and filler parameters (volume fraction, density and diameter) on RBC performance. METHOD Six experimental RBCs modified from a commercial RBC were tested. The three-point flexure strength (σ(3)) and modulus (E) data was determined for groups of 20 bar-shaped...

The 12 C/ 13 C isotope ratio is a tracer of stellar yields and the efficiency of mixing in the ISM. 12 CH + / 13 CH + is not affected by interstellar chemistry, and is the most secure way of measuring 12 C/ 13 C in the diffuse ISM. R = 12 C/ 13 C is 90 in the solar system. Previous measurements of 12 CH + λλ3957.7,4232.3 and 13 CH + λλ3958.2,4232.0 absorption toward nearby stars indicate some v...

It is well-known that the use of a large adaptive gain in model-reference adaptive control (MRAC) can result in poor robustness.1 Two well-known robust modification methods, namely; the σ -modification2 and e-modification,3 have been used extensively. The last decade has seen a surge in many new adaptive control methods such as the L1 adaptive control,4 adaptive loop transfer recovery,5 Kalman ...

porous silicon samples were prepared by electrochemical etching method for different etching times. the structural properties of porous silicon (ps) samples were determined from the atomic force microscopy (afm) measurements. the surface mean root square roughness (σ rms) changes as function of porosity were studied, and the influence of etching time on porosity and roughness was studied too. u...

In the present paper, we introduce a new modification of Szász-Mirakyan operators based on [Formula: see text]-integers and investigate their approximation properties. We obtain weighted approximation and Voronovskaya-type theorem for new operators.