Half-Metallic Ferromagnetism in the Co-Doped CdS Diluted Magnetic Semiconductor

JETP Letters - The magnetic properties of Co-doped CdS has been investigated by ab initio calculations using the GGA + U approximation. The study reveals the ferromagnetic ordering of Co-doped CdS...     

A comparative study of functional equations characterising sine and cosine

A comparative study of the functional equationsf(x+y)f(x–y)=f ²(x)–f ²(y),f(y){f(x+y)+f(x–y)}=f(x)f(2y) andf(x+y)+f(x–y)=2f(x){1–2f ²(y/2)} which characterise the sine function has been carried out. The zeros of the functionf satisfying any one of the above equations play a vital role in the investigations. The relation of the equationf(x+y)+f(x–y)=2f(x){1–2f ²(y/2)} with D'Alembert's equation,f(x+y)+f(x–y)=2f(x)f(y) and the sine-cosine equationg(x–y)=g(x)g(y) +f(x)f(y) has also been investigated.     

Evaluation of a cubic character sum using the √−19 division points of the curve Y2 = X3 − 23 · 19X + 2 · 192

The √?19 division points on the curve y² = f(x) of the title are calculated explicitly and the effect of the Frobenius map on these points is found in order to evaluate the cubic character sum $\text{Σ}{}_{\mathrm{<mtext>x(</mtext><mtext>mod</mtext><mtext>\; p)</mtext>}}\text{(}\text{f(x)}\text{p}\text{)}$.     

On Jensen's functional equation

Summary Letf be a map from a groupG into an abelian groupH satisfyingf(xy) + f(xy ^–1) = 2f(x), f(e) = 0, wherex, y G ande is the identity inG. A set of necessary and sufficient conditions forS(G, H) = Hom(G, H) is given whenG is abelian, whereS(G, H) denotes all the solutions of the functional equation. The case whenG is non-abelian is also discussed.     

On the 4-power stufe of a field

Define the 4-powers ₄ (k) of a fieldk to be the least positive integers for which the equation ?1=a ₁ ⁴ +…+a _s ⁴ is solvable ink (if at all). We determines ₄ (k) whenk is a Galois field and prove some results abouts ₄ (k) whenk is an imaginary quadratic field.     

On an exponential-cosine functional equation

The exponential cosine functional equationf(x + y) + (2f ²(y) – f(2y))f(x – y) = 2f(x)f(y) is studied in some detail whenf is a complex valued function defined on a Banach space. We supply conditions which ensure continuity off everywhere under the hypothesis thatf is continuous at a point. We also find solutions of the functional equation which are continuous at some point.     

Eine Bemerkung über das asymptotische Verhalten von Summen über multiplikative Funktionen

Ohne Zusammenfassung

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