On the Function H (m, a, x ) = exp(− ιx )F (m + 1 − ιa , 2 m + 2; 2ιx

Spotlights: [M+.Crown.Y-] as a reagent (M+= K+, NO+; Y-= Br3-, I3-, H(NO3)2)

Fateme Derakhshan-Panah was born in Hamedan (Iran) in 1987. She received her B.S. in Pure Chemistry (2009) and M.S. in Organic Chemistry (2011) from Bu-Ali Sina University, Iran. She is currently working towards her Ph.D. under the supervision of Professor M. A. Zolfigol. Her research interest is organic methodology especially the application of solid acids and ionic liquids in organic synthesis.

Spotlights: [M+.Crown.Y-] as a reagent (M+= K+, NO+; Y-= Br3-, I3-, H(NO3)2)

Fateme Derakhshan-Panah was born in Hamedan (Iran) in 1987. She received her B.S. in Pure Chemistry (2009) and M.S. in Organic Chemistry (2011) from Bu-Ali Sina University, Iran. She is currently working towards her Ph.D. under the supervision of Professor M. A. Zolfigol. Her research interest is organic methodology especially the application of solid acids and ionic liquids in organic synthesis.

O + + H 2 O „ + M ... \ H 5 O 2 + „ + M ...

On the Exponential Diophantine Equation ( 12 m 2 + 1 ) x + ( 13 m 2 − 1 )

Let m be a positive integer. Then we show that the exponential Diophantine equation (12m2 + 1)x + (13m2 − 1)y = (5m)z has only the positive integer solution (x, y, z) = (1, 1, 2) under some conditions. The proof is based on elementary methods and Baker’s method. Mathematics Subject Classification: 11D61

ar X iv : m at h / 06 05 52 2 v 1 [ m at h . C A ] 1 8 M ay 2 00 6 THE LITTLEWOOD - GOWERS PROBLEM

The paper has two main parts. To begin with suppose that G is a compact Abelian group. Chang’s Theorem can be viewed as a structural refinement of Bessel’s inequality for functions f ∈ L2(G). We prove an analogous result for functions f ∈ A(G), where A(G) := {f ∈ L1(G) : ‖f̂‖1 < ∞} equipped with the norm ‖f‖A(G) := ‖f̂‖1, and generalize this to the approximate Fourier transform on Bohr sets. As a...