Bianchi forms are generalizations of classical modular forms. The arithmetic significance of these forms is revealed through the system eigenvalues determined by a family of linear operators known as Hecke operators.

In this paper, we present a fuzzy logic integration to the Hidden Markov Models (HMM). We have replaced the basic arithmetic operators by some adequate k z y operators. Using fuzzy operators permits us to relax the additivity constraint of probability measures. So we will need only the monotonicity with respect to set inclusion. Some results show the interest of our approach.

‎we obtain the asymptotic expansion of the sequence with general term $frac{a_n}{g_n}$‎, ‎where $a_n$ and $g_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎also‎, ‎we obtain some explicit bounds concerning $g_n$ and $frac{a_n}{g_n}$.

The process of proving some mathematical theorems can be greatly reduced by relying on numericallyintensive computations with a certified arithmetic. This article presents a formalization of floatingpoint arithmetic that makes it possible to efficiently compute inside the proofs of the Coq system. This certified library is a multi-radix and multi-precision implementation free from underflow and...

This article addresses the development of complex, heavily parameterized and flexible operators to be used in FPGA-based floating-point accelerators. Languages such as VHDL or Verilog are not ideally suited for this task. The main problem is the automation of problems such as parameterdirected or target-directed architectural optimization, pipeline optimization, and generation of relevant test ...

In a recent paper by Hirzallah et al. [O. Hirzallah, F. Kittaneh, M. Krnić, N. Lovričević, and J. Pečarić. Eigenvalue inequalities for differences of means of Hilbert space operators. Linear Algebra and its Applications, 436:1516–1527, 2012.], several eigenvalue inequalities are obtained for the difference of weighted arithmetic and weighted geometric means of two positive invertible operators ...

Many algorithms rely on floating point arithmetic for the dynamic range of representations and require millions of calculations per second. Such computationally intensive algorithms are candidates for acceleration using custom computing machines (CCMs) being tailored for the application. Unfortunately, floating point operators require excessive area (or time) for conventional implementations. I...