Multiplicative kernel

Of interest also are the results of applications of the Smoluchowski equation for systems with more complex aggregation physics than that provided by bilinear kernels. Leyvraz and Tschudi [32] conjectured that for the kernel ICy-fi) ) gelation occurs only when co > 1/2. The post-gelation behavior of a general system with a multiplicative kernel given by Eq. (60) has been analyzed by van Don-gen et al. [56]. By assuming that the distribution past the gel point could be expressed through that at t=tc, thus... 

The form and structure of the nut varies with each species. The doum palm produces fruits the size of small oranges, that each hold one kernel (nut), while the tagua produces fruits the size of human heads, that contain multiple kernels. Both types of kernel are about the size of a chicken s egg. The tagua is the nut most used today. 

Gonen M, Alpaydin E (2011) Multiple kernel learning algorithms. J Mach Learn Res... 

As noted above, one of the goals of NAMD 2 is to take advantage of clusters of symmetric multiprocessor workstations and other non-uniform memory access platforms. This can be achieved in the current design by allowing multiple compute objects to run concurrently on different processors via kernel-level threads. Because compute objects interact in a controlled manner with patches, access controls need only be applied to a small number of structures such as force and energy accumulators. A shared memory environment will therefore contribute almost no parallel overhead and generate communication equal to that of a single-processor node. 

The same shipment of raw, cooked and roasted glandless whole kernel cottonseed flours used in the FDA study was used to determine the protein efficiency ratio (PER) of each flour (8). The adjusted PER (Table II) of cooked (2.10) cottonseed was significantly higher than roasted (1.77) cottonseed. Protein retention efficiency (PRE) for roasted cottonseed (58.08) was lower than values for raw (60.54) and cooked (62.95) cottonseed. Relative protein values (RPV) indicated a utilization of 91, 91 and 96% of the protein in raw, roasted and cooked cottonseed, respectively. The multiplication of the (RPV) percentage utilization and the protein content of the cottonseed (Table I) results in the relative utilizable protein values (Table II). 

Lasch EE, El Shawa R. 1981. Multiple cases of cyanide poisoning by apricot kernels in children from Gaza. Pediatrics 68 5-7. 

A major limitation of the dissipative mechanisms involving multiplicative noise —and by extension the iGLE and WiGLE models— is that they involve equilibrium changes only in the strength of the response with respect to the instantaneous friction kernel. They do not involve a change in the response time of the solvent at equilibrium limits. Presumably the response time also changes in some systems, and the inclusion of this variation is a necessary component of the minimal class of models for nonstationary stochastic dynamics. Plow this should be included, however, is an open problem which awaits an answer. 

Let (A, A) be a principally polarized abelian variety over an algebraically closed field k. If the characteristic of k is not equal to the prime p, then the kernel of multiplication by p on A(k) is a finite group isomorphic to (Z/pZ)29. The polarization A induces a nondegenerate alternating pairing A k)[p] x A( )[p] -+ pp(k). Hence, we can try to classify principally polarized abelian varieties with a symplectic basis for the group of points of order p. However, this no longer works in characteristic p. 

Exercise 4.4 Eix a natural number n and show that the set of n x n matrices of determinant one forms a group. Show more generally that the kernel of any group homomorphism is itself a group. Does the set of all matrices (of all finite sizes) of determinant one form a group under the usual matrix multiplication ... 

As a final point, Kapral has discussed the higher collision events where multiple collisions between A and B occur and a near equilibrium spatial distribution is not maintained. He found that the rate kernel was of the form... 

Multiplication by [Pg.47]

Boyer, C. D., and Preiss, J. 1978a. Multiple forms of (1—>4)-a-D-glucan 6-glycosyl transferase from developing Zea mays L. kernels. Carbohydr. Res. 61, 321-334. 

Let G be algebraic of multiplicative type. Show there is a homomorphism from G to a finite group scheme with kernel a torus. 

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