this paper is devoted to the study of establishing sufficient conditions forexistence and uniqueness of positive solution to a class ofnon-linear problems of fractional differential equations. the boundary conditionsinvolved riemann-liouville fractional order derivative and integral. further, the non-linear function $f$ containfractional order derivative which produce extra complexity. thank to...

Algebraic cryptanalysis is as a general framework that permits to assess the security of a wide range of cryptographic schemes. However, the feasibility of algebraic cryptanalysis against block ciphers remains the source of speculation and especially in targeting modern block ciphers. The main problem is that the size of the corresponding algebraic system is so huge (thousand of variables and e...

Matrix differential equation descriptions of the cumulants of an integral quadratic cost associated with a linear system with white-noise input were derived in the mid-70s using generalized Karhunen-Loeve expansion techniques. Here, these same descriptions are derived directly from the cumulant generating function of the cost. A generalization of the k-cumulant control problem class introduced ...

Conventional approach for solving replenishment lot size problem is by using the differential calculus with the need of applying the first-order and second-order differentiations to the long-run average production-inventory cost. A recent published paper used conventional method to determine optimal lot size for an integrated production-delivery system with scrap and cost lessening distribution...

The main contribution of this paper is to provide a classification of disturbance vectors used in differential collision attacks against SHA-1. We show that all published disturbance vectors can be classified into two types of vectors, type-I and type-II. We present a deterministic algorithm which produce efficient disturbance vectors with respect to any given cost function. We define two simpl...

In control theory one is given a system-usually described by differential equations-that can be influenced by an external action. In optimal control problems, such an action is to be exercised for minimizing a given cost functional. The cost functionals of interest may be of very different nature. In general, they may depend on the state of the system, on the control, and possibly on the system...

The correction in value of an OTC derivative contract due to counterparty risk under funding constraints, is represented as the value of a dividend-paying option on the value of the contract clean of counterparty risk and excess funding costs. This representation allows one to analyze the structure of this correction, the so-called Credit Valuation Adjustment (CVA for short), in terms of replac...

This paper presents an algorithm for solving optimal power flow problem through the application of Differential Evolution (DE). The objective is to minimize the total fuel cost of thermal generating units having quadratic cost characteristics subjected to limits on generator real and reactive power outputs, bus voltages, transformer taps and power flow of transmission lines. The proposed method...

We demonstrate that it is possible to train large recurrent language models with user-level differential privacy guarantees with only a negligible cost in predictive accuracy. Our work builds on recent advances in the training of deep networks on user-partitioned data and privacy accounting for stochastic gradient descent. In particular, we add user-level privacy protection to the federated ave...