Let δ be a derivation on R. A ring R is called δ-quasi-Baer (resp. quasi-Baer) if the right annihilator of every δ-ideal (resp. ideal) of R is generated by an idempotent of R. In this note first we give a positive answer to the question posed in Han et al. [7], then we show that R is δ-quasi-Baer iff the differential polynomial ring S = R[x; δ] is quasi-Baer iff S is δ‾-quasi-Baer for every extended derivation δ‾ on S of δ. This results is a generalization of Han et al. [7], to the case where R is not assumed to be δ-semiprime.

en-copyright= kn-copyright= en-aut-name=HashemiEbrahim en-aut-sei=Hashemi en-aut-mei=Ebrahim kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil=Shahrood University of Thechnology END start-ver=1.4 cd-journal=joma no-vol=52 cd-vols= no-issue=1 article-no= start-page=133 end-page=142 dt-received= dt-revised= dt-accepted= dt-pub-year=2010 dt-pub=201001 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A GENERAL INEQUALITY FOR DOUBLY WARPED PRODUCT SUBMANIFOLDS en-subtitle= kn-subtitle= en-abstract= kn-abstract=

In this paper, we consider doubly warped product manifolds and we establish a general inequality for doubly warped products isometrically immersed in arbitrary Riemannian manifolds. Some aplications are derived.

We deal with the following variant of the primitive element theorem: any commutative strongly separable extension of a commutative ring can be embedded in another one having primitive element. This statement holds for connected strongly separable extension of commutative rings which are either local or connected semilocal. We show that it holds for a more general family of rings, that is, for connected commutative rings whose quotient ring by the corresponding Jacobson radical is von Neumann regular and locally uniform. Some properties of the (connected) separable closure of such rings are also given as an application of this result.

en-copyright= kn-copyright= en-aut-name=BagioDirceu en-aut-sei=Bagio en-aut-mei=Dirceu kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= en-aut-name=PaquesAntonio en-aut-sei=Paques en-aut-mei=Antonio kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=2 ORCID= affil-num=1 en-affil= kn-affil=Universidade Federal de Santa Maria affil-num=2 en-affil= kn-affil=Universidade Federal do Rio Grande do Sul en-keyword=primitive element kn-keyword=primitive element en-keyword=von Neumann regular ring kn-keyword=von Neumann regular ring en-keyword=locally uniform ring kn-keyword=locally uniform ring en-keyword=strongly separable extension kn-keyword=strongly separable extension en-keyword=separable closure kn-keyword=separable closure END start-ver=1.4 cd-journal=joma no-vol=40 cd-vols= no-issue=1 article-no= start-page=99 end-page=111 dt-received= dt-revised= dt-accepted= dt-pub-year=1998 dt-pub=199801 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A Generation of the Hopf Construction en-subtitle= kn-subtitle= en-abstract= kn-abstract= en-copyright= kn-copyright= en-aut-name=ShimizuToshiyuki en-aut-sei=Shimizu en-aut-mei=Toshiyuki kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil=Fukuoka University END start-ver=1.4 cd-journal=joma no-vol=47 cd-vols= no-issue=1 article-no= start-page=141 end-page=146 dt-received= dt-revised= dt-accepted= dt-pub-year=2005 dt-pub=200501 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A Lower Bound for the LS Category of a Formal Elliptic Space en-subtitle= kn-subtitle= en-abstract= kn-abstract=

We give a lower bound for the LS category of a formal elliptic space in terms of its rational cohomology.

en-copyright= kn-copyright= en-aut-name=KotaniYasusuke en-aut-sei=Kotani en-aut-mei=Yasusuke kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= en-aut-name=YamaguchiToshihiro en-aut-sei=Yamaguchi en-aut-mei=Toshihiro kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=2 ORCID= affil-num=1 en-affil= kn-affil=Kochi University affil-num=2 en-affil= kn-affil=Kochi University en-keyword=LS category kn-keyword=LS category en-keyword=rationally elliptic space kn-keyword=rationally elliptic space en-keyword=F0-space kn-keyword=F0-space en-keyword= formal. kn-keyword= formal. END start-ver=1.4 cd-journal=joma no-vol=50 cd-vols= no-issue=1 article-no= start-page=201 end-page=203 dt-received= dt-revised= dt-accepted= dt-pub-year=2008 dt-pub=200801 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A Lower Bound for the Rational LS-category of a Coformal Elliptic Space en-subtitle= kn-subtitle= en-abstract= kn-abstract=

We give a lower bound for the rational LS-category of certain spaces, including the coformal elliptic ones, in terms of the dimension of its total rational cohomology.

We give some new properties of almost injective modules and their endomorphism rings, and also provide conditions as to when a direct sum of almost injective (or CS) modules is again almost injective (or CS) in some special cases..

en-copyright= kn-copyright= en-aut-name=AlahmadiAdel en-aut-sei=Alahmadi en-aut-mei=Adel kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= en-aut-name=JainSurender K. en-aut-sei=Jain en-aut-mei=Surender K. kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=2 ORCID= affil-num=1 en-affil= kn-affil=Department of Mathematics, Ohio University affil-num=2 en-affil= kn-affil=Department of Mathematics, Ohio University END start-ver=1.4 cd-journal=joma no-vol=51 cd-vols= no-issue=1 article-no= start-page=193 end-page=201 dt-received= dt-revised= dt-accepted= dt-pub-year=2009 dt-pub=200901 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A NOTE ON CERTAIN METRICS ON R4+ en-subtitle= kn-subtitle= en-abstract= kn-abstract= en-copyright= kn-copyright= en-aut-name=OtsukiTominosuke en-aut-sei=Otsuki en-aut-mei=Tominosuke kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil= END start-ver=1.4 cd-journal=joma no-vol=52 cd-vols= no-issue=1 article-no= start-page=89 end-page=95 dt-received= dt-revised= dt-accepted= dt-pub-year=2010 dt-pub=201001 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A NOTE ON QUASI-ARMENDARIZ RINGS en-subtitle= kn-subtitle= en-abstract= kn-abstract=

A ring R is called a quasi-Armendariz ring if whenever elements α = a0+a1x+a2x2+· · ·+anxn, β = b0+b1x+b2x2+· · ·+bmxm ∈ R[x] satisfy αR[x]β = 0, then aiRbj = 0 for each i, j. In this note we consider quasi-Armendariz property of a special subring of the infinite upper triangular matrix ring over a ring R.

en-copyright= kn-copyright= en-aut-name=ZhongkuiLiu en-aut-sei=Zhongkui en-aut-mei=Liu kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= en-aut-name=WenhuiZhang en-aut-sei=Wenhui en-aut-mei=Zhang kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=2 ORCID= affil-num=1 en-affil= kn-affil=Department of Mathematics, Northwest Normal University affil-num=2 en-affil= kn-affil=Department of Mathematics, Northwest Normal University en-keyword=Armendariz ring kn-keyword=Armendariz ring en-keyword=quasi-Armendariz ring kn-keyword=quasi-Armendariz ring en-keyword=left APP-ring kn-keyword=left APP-ring END start-ver=1.4 cd-journal=joma no-vol=50 cd-vols= no-issue=1 article-no= start-page=1 end-page=61 dt-received= dt-revised= dt-accepted= dt-pub-year=2008 dt-pub=200801 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A New Class of Quasicyclic Complex Vector Functional Equations en-subtitle= kn-subtitle= en-abstract= kn-abstract=

For the first time in the literature a quasicyclic complex vector functional equation is introduced in the present paper. By a matrix method the general quasicyclic complex vector functional equation is solved, as well as its particular case for n = 3. This case is completely solved in an explicit form, and for every step of the solution examples are provided. Using a simple spectral property of compound matrices, a necessary and sufficient condition for stability of the quasicyclic complex vector functional equation considered is proved.

en-copyright= kn-copyright= en-aut-name=RisteskiIce B. en-aut-sei=Risteski en-aut-mei=Ice B. kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil= en-keyword=Quasicyclic complex vector functional equation kn-keyword=Quasicyclic complex vector functional equation END start-ver=1.4 cd-journal=joma no-vol=48 cd-vols= no-issue=1 article-no= start-page=173 end-page=180 dt-received= dt-revised= dt-accepted= dt-pub-year=2006 dt-pub=200601 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A New Generalization of the Poisson Kernel en-subtitle= kn-subtitle= en-abstract= kn-abstract=

The purpose of this paper is to give a new generalization of the Poisson Kernel in two dimensions and discuss an integral formula for this.

en-copyright= kn-copyright= en-aut-name=BulutSerap en-aut-sei=Bulut en-aut-mei=Serap kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil=Balikesir University en-keyword=Poisson Kernel kn-keyword=Poisson Kernel en-keyword=Integral Formula kn-keyword=Integral Formula END start-ver=1.4 cd-journal=joma no-vol=37 cd-vols= no-issue=1 article-no= start-page=137 end-page=151 dt-received= dt-revised= dt-accepted= dt-pub-year=1995 dt-pub=199501 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A Non-immersion Result for Lens Spaces Ln(2m) en-subtitle= kn-subtitle= en-abstract= kn-abstract= en-copyright= kn-copyright= en-aut-name=JunodBernard en-aut-sei=Junod en-aut-mei=Bernard kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil=Université De Neuchâtel END start-ver=1.4 cd-journal=joma no-vol=32 cd-vols= no-issue=1 article-no= start-page=7 end-page=11 dt-received= dt-revised= dt-accepted= dt-pub-year=1990 dt-pub=199001 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A Note on Anderson-Anderson-Johnson Questions en-subtitle= kn-subtitle= en-abstract= kn-abstract= en-copyright= kn-copyright= en-aut-name=MatsudaRyuki en-aut-sei=Matsuda en-aut-mei=Ryuki kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil=Ibaraki University END start-ver=1.4 cd-journal=joma no-vol=46 cd-vols= no-issue=1 article-no= start-page=121 end-page=130 dt-received= dt-revised= dt-accepted= dt-pub-year=2004 dt-pub=200401 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A Note on Commutative Gelfand Theory for Real Banach Algebras en-subtitle= kn-subtitle= en-abstract= kn-abstract=

Pfaffenberger and Phillips [2] consider a real and unital case of the classical commutative Gelfand theorem and obtain two representation theorems. One is to represent a unital real commutative Banach algebra A as an algebra of continuous functions on the unital homomorphism space ΦA. The other is to represent A as an algebra of continuous sections on the maximal ideal space MA. In this note, we point out that similar theorems for non-unital case hold and show that two representation theorems are essentially identical.

en-copyright= kn-copyright= en-aut-name=TakahashiSin-Ei en-aut-sei=Takahashi en-aut-mei=Sin-Ei kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= en-aut-name=MiuraTakeshi en-aut-sei=Miura en-aut-mei=Takeshi kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=2 ORCID= en-aut-name=HatoriOsamu en-aut-sei=Hatori en-aut-mei=Osamu kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=3 ORCID= affil-num=1 en-affil= kn-affil=Yamagata University affil-num=2 en-affil= kn-affil=Yamagata University affil-num=3 en-affil= kn-affil=Niigata University, Niigata en-keyword=real commutative Banach algebras kn-keyword=real commutative Banach algebras en-keyword=real algebra homomorphisms kn-keyword=real algebra homomorphisms en-keyword= commutative Gelfand theory. kn-keyword= commutative Gelfand theory. END start-ver=1.4 cd-journal=joma no-vol=32 cd-vols= no-issue=1 article-no= start-page=83 end-page=88 dt-received= dt-revised= dt-accepted= dt-pub-year=1990 dt-pub=199001 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A Note on Derivations en-subtitle= kn-subtitle= en-abstract= kn-abstract= en-copyright= kn-copyright= en-aut-name=BrešarMatej en-aut-sei=Brešar en-aut-mei=Matej kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil=University of Ljubljana END start-ver=1.4 cd-journal=joma no-vol=31 cd-vols= no-issue=1 article-no= start-page=85 end-page=91 dt-received= dt-revised= dt-accepted= dt-pub-year=1989 dt-pub=198901 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A Note on Fixed Rings en-subtitle= kn-subtitle= en-abstract= kn-abstract= en-copyright= kn-copyright= en-aut-name=KitamuraYoshimi en-aut-sei=Kitamura en-aut-mei=Yoshimi kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil=Tokyo Gakugei University END start-ver=1.4 cd-journal=joma no-vol=45 cd-vols= no-issue=1 article-no= start-page=145 end-page=162 dt-received= dt-revised= dt-accepted= dt-pub-year=2003 dt-pub=200301 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A Note on Geodesics and Curvatures of Certain 4-spaces en-subtitle= kn-subtitle= en-abstract= kn-abstract=

This work is a continuation of the papers [3] and [4], in which we studied the metrics (1.1) and (1.2) on R4+. The metric (1.1) with a = 0: ds2 = dx1dx1 + dx2dx2 + dx3dx3 − dx4dx4 x4x4 is analogous to the metric of the hyperbolic 4-space. We considered fundamentally metrics on R4+ based on this hyperbolic type metric, not Euclidean or Minkowsky types.

en-copyright= kn-copyright= en-aut-name=OtsukiTominosuke en-aut-sei=Otsuki en-aut-mei=Tominosuke kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil= END start-ver=1.4 cd-journal=joma no-vol=41 cd-vols= no-issue=1 article-no= start-page=15 end-page=19 dt-received= dt-revised= dt-accepted= dt-pub-year=1999 dt-pub=199901 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A Note on Osofsky-Smith Theorem en-subtitle= kn-subtitle= en-abstract= kn-abstract= en-copyright= kn-copyright= en-aut-name=ZhongkuiLiu en-aut-sei=Zhongkui en-aut-mei=Liu kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil=Northwest Normal University END start-ver=1.4 cd-journal=joma no-vol=47 cd-vols= no-issue=1 article-no= start-page=159 end-page=162 dt-received= dt-revised= dt-accepted= dt-pub-year=2005 dt-pub=200501 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A Note on Quotients of Orthogonal Groups en-subtitle= kn-subtitle= en-abstract= kn-abstract=

We discuss the mod 2 cohomology of the quotient of a compact classical Lie group by its maximal 2-torus. In particular, the case of the orthogonal group is treated. The case of the spinor group is not included.

en-copyright= kn-copyright= en-aut-name=OhsitaAkihiro en-aut-sei=Ohsita en-aut-mei=Akihiro kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil=Osaka University of Economics en-keyword=Lie group kn-keyword=Lie group en-keyword=cohomology kn-keyword=cohomology en-keyword=2-torsion kn-keyword=2-torsion en-keyword= 2-root. kn-keyword= 2-root. END start-ver=1.4 cd-journal=joma no-vol=32 cd-vols= no-issue=1 article-no= start-page=73 end-page=76 dt-received= dt-revised= dt-accepted= dt-pub-year=1990 dt-pub=199001 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A Note on Zero Commutative and Duo Rings en-subtitle= kn-subtitle= en-abstract= kn-abstract= en-copyright= kn-copyright= en-aut-name=HabebJebrel M. en-aut-sei=Habeb en-aut-mei=Jebrel M. kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil=Yarmouk University END start-ver=1.4 cd-journal=joma no-vol=42 cd-vols= no-issue=1 article-no= start-page=153 end-page=160 dt-received= dt-revised= dt-accepted= dt-pub-year=2000 dt-pub=200001 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A Note on the Degenerate Morse Inequalities en-subtitle= kn-subtitle= en-abstract= kn-abstract=

In this paper we give an analytic proof of the degenerate Morse inequalities in the spirit of E. Witten. The max-min methods are used to estimate the number of ‘small’ eigenvalues of Witten’s deformed Laplacian.

We give a complete representation of a ring homomorphism from a unital semisimple regular commutative Banach algebra into a unital semisimple commutative Banach algebra, which need not be regular. As a corollary we give a sufficient condition in order that a ring homomorphism is automatically linear or conjugate linear.

en-copyright= kn-copyright= en-aut-name=MiuraTakeshi en-aut-sei=Miura en-aut-mei=Takeshi kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil=Yamagata University en-keyword=commutative Banach algebras kn-keyword=commutative Banach algebras en-keyword= ring homomorphisms. kn-keyword= ring homomorphisms. END start-ver=1.4 cd-journal=joma no-vol=46 cd-vols= no-issue=1 article-no= start-page=131 end-page=140 dt-received= dt-revised= dt-accepted= dt-pub-year=2004 dt-pub=200401 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A Study of Fq-Functions Connected with Ramanujan's Tenth Order Mock Theta Functions en-subtitle= kn-subtitle= en-abstract= kn-abstract=

<P>We have defined generalized functions which reduce to Ramanujan's mock theta functions of order ten. We have shown that they are Fq-functions. We have given their integral representation and multibasic expansions.

We combine various well-known techniques from the theory of heights, the theory of “noncritical Belyi maps”, and classical analytic number theory to conclude that the “ABC Conjecture”, or, equivalently, the so-called “Effective Mordell Conjecture”, holds for arbitrary rational points of the projective line minus three points if and only if it holds for rational points which are in “sufficiently general position” in the sense that the following properties are satisfied: (a) the rational point under consideration is bounded away from the three points at infinity at a given finite set of primes; (b) the Galois action on the l-power torsion points of the corresponding elliptic curve determines a surjection onto GL2(Zl), for some prime number l which is roughly of the order of the sum of the height of the elliptic curve and the logarithm of the discriminant of the minimal field of definition of the elliptic curve, but does not divide the conductor of the elliptic curve, the rational primes that are absolutely ramified in the minimal field of definition of the elliptic curve, or the local heights [i.e., the orders of the q-parameter at primes of [bad] multiplicative reduction] of the elliptic curve.

This paper is concerned with the existence and uniqueness of almost periodic mild solutions of evolution equations of the form u(t) = Au(t) + ƒ(t) where A is the generator of a holomorphic Csemigroup on a Banach space and ƒ is an almost periodic function. A sufficient condition in terms of spectral properties of A and ƒ is obtained that extends a well known result in this subject.

In this paper we present an explicit construction of Belyi functions whose dessins are flower trees (i.e., graphs of diameter 4) with two ramification indices. We also give a method for obtaining Belyi functions defined over the moduli fields of the dessins.

Let F be a field of char(F) = p > 0 and G an abelian group with p-component Gp of cardinality at most ℵ1 and length at most ω1. The main affirmation on the Direct Factor Problem is that S(FG)/Gp is totally projective whenever F is perfect. This extends results due to May (Contemp. Math., 1989) and Hill-Ullery (Proc. Amer. Math. Soc., 1990). As applications to the Isomorphism Problem, suppose that for any group H the F-isomorphism FH ≅ FG holds. Then if Gp is totally projective, Hp ≅ Gp. This partially solves a problem posed by May (Proc. Amer. Math. Soc., 1988). In particular, H ≅ G provided G is p-mixed of torsion-free rank one so that Gp is totally projective. The same isomorphism H ≅ G is fulfilled when G is p-local algebraically compact too. Besides if Fp is the simple field with p-elements and Gp FpH is a coproduct of torsion complete groups, FpH ≅ FpG as Fp Fp-algebras implies Hp ≅ Gp. This expands the central theorem obtained by us in (Rend. Sem. Mat. Univ. Padova, 1999) and partly settles the generalized version of a question raised by May (Proc. Amer. Math. Soc.,1979) as well. As a consequence, when Gp is torsion complete and G is p-mixed of torsion-free rank one, H ≅ G. Moreover, if G is a coproduct of p-local algebraically compact groups then H ≅ G. The last attainment enlarges an assertion of Beers-Richman-Walker (Rend. Sem. Mat. Univ. Padova, 1983). Each of the reported achievements strengthens our statements in this direction (Southeast Asian Bull. Math., 2001-2002) and also continues own studies in this aspect (Hokkaido Math. J., 2000) and (Kyungpook Math. J., 2004).

We studied the pseudo-Riemannian metric on R3 × R+, where γ2 = Σ3b=1xbxb and a = constant, which satisfies the Einstein condition (in [1], [2], [3] ). The purpose of this work is to find Einstein metrics including the above metric as a special one, which is analogous to the relation between the Schwarzschild metric and the Kerr one in the theory of relativity.

en-copyright= kn-copyright= en-aut-name=OtsukiTominosuke en-aut-sei=Otsuki en-aut-mei=Tominosuke kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil= END start-ver=1.4 cd-journal=joma no-vol=43 cd-vols= no-issue=1 article-no= start-page=143 end-page=184 dt-received= dt-revised= dt-accepted= dt-pub-year=2001 dt-pub=200101 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=Certain Metrics on R4+(II) en-subtitle= kn-subtitle= en-abstract= kn-abstract=

This paper is a continuation of the one with the same title([4]), in which we obtained a special solution for a system of differential equations on metric tensors on R4+ satisfying the Einstein condition for Case I generalizing the Ot-metric: in Theorem 1, and proved that there exist no solutions for Case II in Theorem 2. In this work, we shall show that we can obtain more general solutions for Case I which depend on the latitude parameter. We use the results in [4], so the section numbers start from 5. 1. Preliminaries and curvature tensor 2. Ricci tensor 3. Solutions for Case I 4. Analysis and a conclusion for Case II

We define a Con-Cos group G to be one having a proper normal subgroup N whose cosets other than N itself are conjugacy classes. It follows easily that N = G’, the derived group of G. Most of the paper is devoted to trying to classify finite Con-Cos groups satisfying the additional requirement that N has just two conjugacy classes. We show that for such groups the center Z(G) has order at most 2, and if Z(G) = {1}, then G is a Frobenius group of a rather special type.