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Algebraic monoids with affine unit group are affine
      
In this short paper we prove that any irreducible algebraic monoid whose unit group is an affine algebraic group is affine.
      
One outcome is a simple proof that for $g_{m \alpha , n \beta}$ to span $L^2,$ the lattice $(m \alpha , n \beta )$ must have at least unit density.
      
This is done by proving that a well-known method, the construction of a Perron Tree, can be applied to a larger collection of subsets of the unit circle than was earlier known.
      
In the special case of Ω=Id, the d-dimensional unit cube, we prove this conjecture, with Ω'=Id, for d≤3, describing all the tilings by Id, and for all d when Λ is a discrete periodic set.
      
For p∈(-∞, ∞) letQp(?Δ) be the space of all complex-valued functions f on the unit circle ?Δ satisfying, where the supremum is taken over all subarcs I ? ?Δ with the arclength |I|.
      
In this article we consider a simple method of radial quasi-interpolation by polynomials on the unit sphere in ?3, and present rates of covergence for this method in Sobolev spaces of square integrable functions.
      
This description is based on a one-to-one correspondence between the set of all solutions of the Covariance Extension Problem and the set of all contractive analytic functions H from the open unit disk with values on the space of q × q matrices.
      
Toeplitz operators on the Bergman space of the unit disc can be written as integrals of the symbol against an invariant operator field of rank-one projections.
      
We present a method for constructing wavelet bases on the unit sphere S2 of R3, using the radial projection and an inner product associated to a convex polyhedron having the origin inside.
      
We prove two probabilistic versions of Hardy's inequality concerning the Fourier coefficients of an integrable function on the unit circle.
      
For this purpose we study in detail the properties of the restriction of Fourier transform on the unit cotangent sphere associated with the symbols of?multipliers.
      
On the basis of total acid hydrolysis, methylation analysis, periodate oxidation and NMR studies (1H and 13C) the structure of the repeating unit of the polysaccharide was assigned and indicated only α-(1→4) linked Glucan.
      
The structural information of the glucan was achieved by chemical (hydrolysis, methylation, periodate oxidation) and spectroscopic (1H and 13C) analyses, indicated a repeating unit built up of (1→6)-linked D-glucose.
      
The following structure has been determined for the repeating unit: →6)-α-D-Glcp-(1→ This fraction exhibited significant macrophage activity through the release of nitric oxide
      
In previous work, under some assumptions, we specified a replacement rule which minimizes the long-run (expected) average cost per unit time and possesses control limit property.
      
In [7], the author defined a matrix by using r-normal subdivision of the n-dimensional unit cube, considered it a Markov matrix, and constructed the invariant set and invariant measure.
      
Suppose H is a complex Hilbert space, AH (Δ) denotes the set of all analytic operator function on Δ, and the set NH (Δ)={f(z)/f(z) is an analytic operator function on the open unit disk Δ, f(z)f(w)=f(w)f(z), f*(z)f(z)=f(z)f*(z), ? z, w ≡ δ }.
      
The X-ray diffraction results indicate that the melt-crystallized sample of polyamide 618 transforms from the triclinic unit cell to the pseudo-hexagonal phase in the range of 120-180°C.
      
The progress of synthesis and molecular structure design and synthesis of polycarboxylate superplasticizer were reviewed according to the difference in the structure unit of the main chain.
      
 

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