V. L. KLEE, JR. 1 Carmichael [ l ] 2 conjectured that for no integer n can the equation (x)=n ( being Euler's totient) have exactly one solution. To support the conjecture, he showed that each n for which there is a unique solution must satisfy a restriction which implies w>10. In this note we prove the validity of restrictions considerably stronger than those of Carmichael, and raise the...

In this paper, we investigate the Fourier coefficients of eta-quotients forms q λ 0 + l k 1 24 η ( τ ) − , $$ {q}^{\frac{\lambda_0+{l}^k{\lambda}_1}{24}}\eta {\left(\tau \right)}^{-{\lambda}_0}\eta {\left({l}^k\tau \right)}^{-{\lambda}_1}, where \eta \left(\tau \right) is Dedekind eta function, = 5,7 11 13 l=5,7,11,13 and 17; a positive integer, {\lambda}_0,{\lambda}_1 are arbitrary integers. W...

for a composition $lambda$ of $n$ our aim is to obtain reduced forms ‎for all the elements in the kazhdan-lusztig (right) cell containing ‎$w_{j(lambda)}$‎, ‎the longest element of the standard parabolic‎ ‎subgroup of $s_n$ corresponding to $lambda$‎. ‎we investigate how far this is possible to achieve by looking at‎ ‎elements of the form $w_{j(lambda)}d$‎, ‎where $d$ is a prefix of ‎an element...

Lambda lifting is a technique for transforming a program with local function definitions into a program consisting only of global function definitions. The best known lambda lifting algorithm computes the minimal set of extraneous parameters needed by each function in O(n) steps by solving a system of set equations which are recursive if the functions in the program are mutually recursive. Mutu...

A model developed recently by Loisel and Stramski [Appl. Opt. 39, 3001-3011 (2000)] for estimating the spectral absorption a(lambda), scattering b(lambda), and backscattering b(b)(lambda) coefficients in the upper ocean from the irradiance reflectance just beneath the sea surface R(lambda, z = 0(-)) and the diffuse attenuation of downwelling irradiance within the surface layer ?K(d)(lambda)?(1)...

We investigate the transverse polarization of $\Lambda$ hyperon in processes $e^+e^-\to\Lambda^\uparrow \pi^\pm X$ and K^\pm within framework momentum dependent~(TMD) factorization. The is contributed by convolution transversely polarizing fragmentation function~(PFF) $D_{1T}^\perp$ lambda unpolarized function $D_1$ pion/kaon. adopt spectator diquark model result for $D_{1T}^{\perp}$ to numeric...