Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userComplex Differential Spaces
الفضاءات التفاضلية المركبة
499
0 5
0
(
0
)
Added by
Damascus University ورقة بحثية
Publication date
2003
fields
Mathematics
and research's language is
العربية
Created by
Shamra Editor
Ask ChatGPT about the research
تم تعريف صنف من الفضاءات التفاضلية المركبة (العقدية) بطريقة طبيعية. كما تم تعريف مفهوم الدالة الملساء، المتجه المماسي، الحقل المتجهى على هذا الفضاء بطريقة يمكن معها صياغة المفاهيم الأساسية الأخرى للهندسة التفاضلية .
A class of complex differential spaces is defined in a natural way. The notions of smooth mapping, tangent vectors and vector fields on these spaces are introduced, so that the fundamental notions in differential geometry can be formulated.
References used
Raoul Bott, S. S. Chern, “ Hermitian vector bundles and the equi distribution of the zeroes of their holomorphic sections, “ Acta Math.,1965
S. S. Chern, “ Differential geometry of fibre bundles, “ Proc. Of the International Conf. Of Mathematicians, II1950
J. Gruszczak, M. Heller, “Differential structures of space – time and its prolongation to singular boundaries, “ International Journal of Theoretical Physics,1993
rate research
Read More
In this work, we present programming solutions for some nonlinear partial differential equations, which are the advection equation, the third-order KdV
equations, and a family of Burgers' equations.
In this paper, we present a numerical algorithm for solving linear integro differential Volterra-Friedholm equations by using spline polynomials of degree ninth with six collocation points. The Fredholm-Volterra equation is converted into a system of
first-order linear differential equations, which is solved by applying polynomials and their derivatives with collocation points. The convergence of the proposed method is demonstrated when it is applied to above problem. To test the effectiveness and accuracy of this method, two test problems were resolved where comparisons could be used with other results taken from recent references to the high resolution provided by spline approximations.
The robustness and security of natural language processing (NLP) models are significantly important in real-world applications. In the context of text classification tasks, adversarial examples can be designed by substituting words with synonyms unde
r certain semantic and syntactic constraints, such that a well-trained model will give a wrong prediction. Therefore, it is crucial to develop techniques to provide a rigorous and provable robustness guarantee against such attacks. In this paper, we propose WordDP to achieve certified robustness against word substitution at- tacks in text classification via differential privacy (DP). We establish the connection between DP and adversarial robustness for the first time in the text domain and propose a conceptual exponential mechanism-based algorithm to formally achieve the robustness. We further present a practical simulated exponential mechanism that has efficient inference with certified robustness. We not only provide a rigorous analytic derivation of the certified condition but also experimentally compare the utility of WordDP with existing defense algorithms. The results show that WordDP achieves higher accuracy and more than 30X efficiency improvement over the state-of-the-art certified robustness mechanism in typical text classification tasks.
NLP models are vulnerable to data poisoning attacks. One type of attack can plant a backdoor in a model by injecting poisoned examples in training, causing the victim model to misclassify test instances which include a specific pattern. Although defe
nces exist to counter these attacks, they are specific to an attack type or pattern. In this paper, we propose a generic defence mechanism by making the training process robust to poisoning attacks through gradient shaping methods, based on differentially private training. We show that our method is highly effective in mitigating, or even eliminating, poisoning attacks on text classification, with only a small cost in predictive accuracy.
In this paper: the Daubechies families of wavelets Daubechies
and multi resolution analysis based on Fast Fourier Transform
algorithm (FWT) have been applied to solve some differential
equations with Boundary Value.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
