Bordered symmetric square roots of the identity matrix

1976 ◽  
pp. 177-184
Author(s):  
C. E. M. Pearce
Keyword(s):  
Identity Matrix ◽  
Square Roots ◽  
Symmetric Square

scholarly journals Symmetric square roots of the infinite identity matrix

1976 ◽  
Vol 22 (3) ◽  
pp. 343-361
Author(s):  
C. E. M. Pearce ◽  
R. B. Potts
Keyword(s):  
Integral Transforms ◽  
Identity Matrix ◽  
Square Roots ◽  
Symmetric Square

AbstractSome non-trivial real, symmetric square roots of the infinite identity matrix are exhibited. These may be found either from the use of involutory integral transforms and a set of real orthonormal functions or by an algebraic factorisation procedure. The two approaches are shown to be equivalent.

The Singular Value Decomposition of the Square Roots of the Identity Matrix

1995 ◽  
Vol 11 (3) ◽  
pp. 648-653
Author(s):  
Jacob Goeree ◽  
Heinz Neudecker ◽  
S.W. Drury ◽  
George P.H. Styan
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Identity Matrix ◽  
Square Roots ◽  
Value Decomposition

scholarly journals Algebraic singularities of scattering amplitudes from tropical geometry

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
James Drummond ◽  
Jack Foster ◽  
Ömer Gürdoğan ◽  
Chrysostomos Kalousios
Keyword(s):  
Scattering Amplitudes ◽  
Natural Language ◽  
Tropical Geometry ◽  
Cluster Algebras ◽  
Finite Alphabet ◽  
Square Root ◽  
Finite Sets ◽  
Yang Mills ◽  
Square Roots ◽  
Algebraic Singularities

Abstract We address the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory. We argue that connections between cluster algebras and tropical geometry provide a natural language for postulating a finite alphabet for scattering amplitudes beyond six and seven points where the corresponding Grassmannian cluster algebras are finite. As well as generating natural finite sets of letters, the tropical fans we discuss provide letters containing square roots. Remarkably, the minimal fan we consider provides all the square root letters recently discovered in an explicit two-loop eight-point NMHV calculation.

scholarly journals On Fourier Coefficients of the Symmetric Square L-Function at Piatetski-Shapiro Prime Twins

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1254
Author(s):  
Xue Han ◽  
Xiaofei Yan ◽  
Deyu Zhang
Keyword(s):  
Asymptotic Formula ◽  
Fourier Coefficient ◽  
Cusp Form ◽  
Riemann Hypothesis ◽  
Modular Group ◽  
Fourier Coefficients ◽  
Mean Value ◽  
Symmetric Square ◽  
The Mean ◽  
Almost All

Let Pc(x)={p≤x|p,[pc]areprimes},c∈R+∖N and λsym2f(n) be the n-th Fourier coefficient associated with the symmetric square L-function L(s,sym2f). For any A>0, we prove that the mean value of λsym2f(n) over Pc(x) is ≪xlog−A−2x for almost all c∈ε,(5+3)/8−ε in the sense of Lebesgue measure. Furthermore, it holds for all c∈(0,1) under the Riemann Hypothesis. Furthermore, we obtain that asymptotic formula for λf2(n) over Pc(x) is ∑p,qprimep≤x,q=[pc]λf2(p)=xclog2x(1+o(1)), for almost all c∈ε,(5+3)/8−ε, where λf(n) is the normalized n-th Fourier coefficient associated with a holomorphic cusp form f for the full modular group.

scholarly journals Finding of principle square root of a real number by using interpolation method

2018 ◽  
Vol 7 (1) ◽  
pp. 77-83
Author(s):  
Rajendra Prasad Regmi
Keyword(s):  
Real Number ◽  
Positive Real Number ◽  
Interpolation Method ◽  
Square Root ◽  
Real Numbers ◽  
Positive Real ◽  
Unknown Quantity ◽  
Square Roots

There are various methods of finding the square roots of positive real number. This paper deals with finding the principle square root of positive real numbers by using Lagrange’s and Newton’s interpolation method. The interpolation method is the process of finding the values of unknown quantity (y) between two known quantities.

Why Square Roots are Irrational

1986 ◽  
Vol 93 (3) ◽  
pp. 213-214 ◽  
Author(s):  
William C. Waterhouse
Keyword(s):  
Square Roots

scholarly journals On the minimum gap between sums of square roots of small integers

2011 ◽  
Vol 412 (39) ◽  
pp. 5458-5465
Author(s):  
Qi Cheng ◽  
Yu-Hsin Li
Keyword(s):  
Square Roots
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