Can we factor an integer $$N$$ unconditionally, in deterministic polynomial time, given the value of its Euler totient $$\varphi (N)$$ ? We show that this can be done under certain size conditions on prime factors . The key technique is lattice basis reduction using LLL algorithm. Among our results, if has a $$p > \sqrt{N}$$ , then recover $$p$$ time also shed some light analogous factorization...

Solving an integer least squares (ILS) problem usually consists of two stages: reduction and search. This thesis is concerned with the reduction process for the ordinary ILS problem and the ellipsoid-constrained ILS problem. For the ordinary ILS problem, we dispel common misconceptions on the reduction stage in the literature and show what is crucial to the efficiency of the search process. The...

Rice bran is a simple item that delivers fantastic health benefits in our daily diet. This study delivers the importance of utilising all parts of the whole grain, including the bran. The objective was to develop the recipes incorporated with rice bran and evaluate their organoleptic properties and estimate their glycemic index. Ten standard Indian subcontinent recipes namely, chapati, mixed ve...

The aim of this paper is a reduction algorithm for a basis b1, b2, b3 of a 3-dimensional lattice in R n for fixed n ≥ 3. We give a definition of the reduced basis which is equivalent to that of the Minkowski reduced basis of a 3-dimensional lattice. We prove that for b1, b2, b3 ∈ Z, n ≥ 3 and |b1|, |b2|, |b3| ≤ M , our algorithm takes O(log M) binary operations, without using fast integer arith...

lll

???? ??????????? – ????????? ? ???????????? ?????????? ???????? ???????? ???????????? ???????? ???????? ?????? ???????? ???????????. ???????? ??????. ? ?????? ??????????? ???????? ?????? ??????????? 12-13 ????? ?????????????? ????????–????????? ????? l-lll ???????? (9 ??????????? ?????? ???????????????? ?????, 9 ??????????). ??? ?????????? ?????????????? ??????????? ??????????????? ???????? ???...

This chapter introduces Inductive Logic Programming (ILP) and Learning Language in Logic (LLL). No previous knowledge of logic programming, ILP or LLL is assumed. Elementary topics are covered and more advanced topics are discussed. For example, in the ILP section we discuss subsumption, inverse resolution, least general generalisation, relative least general generalisation, inverse entailment,...

We present a method for  the construction of compactlysupported $left (begin{array}{lll}1 & 0 & -1\1 & 1 & 0 \1 &  0 & 1\end{array}right )$-wavelets  under a mild condition. Wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. As an application, an  example is  provided.

Gold(Ill) is isoelectronic (5d8) and often isostructuml (square-planar) with Pt(ll) and might form the basis of active anticancer agents [1]. However little is known about the biochemistry of Au(lll), a subject also of interest in connection with the side-effects of antiarthritic gold drugs [2]. In this work we have explored the binding of [Au(lll)(diethylenetriamine)CI]CI2 to tripeptides over ...