bluuebunny/crossref_metadata_2025 huggingface dataset:
Synthesis of (4-chlorobenzylidene)-(2-chloropyridi-3-yl)amine
Authors: Jarrahpour A. A. , Zarei M.
Published: April 2009

Schiff bases are widely in use for synthetic purposes both by organic and inorganic chemists.[...]
6,10,14,18-Tetramethyl-1,5,10,14,19,20-hexaaza-tricyclo[14.2.1.15,8]eicosa-6,8(20),16(19),17-tetraene
Authors: Touzani Rachid , Ramdani Abdelkrim , El Kadiri Sghir
Published: April 2009

Macrocyclic chemistry is one of the fastest growing fields in chemistry.[...]
7,11,15,19-Tetramethyl-1,6,11,15,20,21-hexaaza-tricyclo[15.2.1.16,9]heneicosa-7,9(21),17(20),18-tetraene
Authors: Touzani Rachid , Ramdani Abdelkrim , El Kadiri et Sghir
Published: April 2009

Despite the numerous polydentate macrocyclic structures already described as neutral receptors for various substrates [1,2,3], the search for new receptor families is still important with a view to obtaining molecules capable of molecular recognition, transport, selective catalysis, and biological models.[...]
7,19-Dimethyl-11,15-bis(pyridin-2-ylmethyl)-1,6,11,15,20,21-hexaaza-tricyclo[15.2.1.16,9]heneicosa-7,9(21),17(20),18-tetraene
Authors: Touzani Rachid , Ramdani Abdelkrim , El Kadiri Sghir
Published: April 2009

Despite the numerous polydentate macrocyclic structures already described as neutral receptors for various substrates [1,2,3], the search for new receptor families is still important with a view to obtaining molecules capable of molecular recognition, transport, selective catalysis or biological models.[...]
Synthesis of antifungal isoindole (5-methyl-isoxazole-3-yl)-[2-(5-methyl-isoxazol-3-yl)2,3-dihydro-isoindol-1-ylidene]amine
Authors: Al-Shihry Shar
Published: April 2009

A large number of isoindoline skeletons such as staurosporine, indoprofen, and pazinaclone have been reported to possess biological activities [1,2,3,4,5].[...]
Synthesis of 4H-3,1-benzoxazin-4-one 2-phenyl Using Cyanuric Chloride as a Cyclization Agent
Authors: Abdollahi Sohrab , Shariat Mehdi
Published: April 2009

The preparation of different derivatives of benzoxazinone can be considered important because they have different kinds of pharmaceutical, agricultural and industrial applications [1,2,3,4].[...]
New bis-tridentate Nitrogen Ligand: N,N,N',N'-tetra-(3-carbomethoxy-5-methylpyrazol-1-ylmethyl)p-phenylenediamine
Authors: Daoudi Maria , Bennani Brahim , Zahidi Assou , Mchich Mohamed , Ben Hadda Taibi
Published: April 2009

The product 2 was prepared by the addition of p-phenylendiamine (NH2C6H4NH2) to 1 [1] according to the reported procedure [2].[...]
Synthesis of New bis-Bidentate Nitrogen Ligand: 1,4-bis[(3,5-dimethyl-1H-pyrazol-1-yl)methyl]piperazine
Authors: El Fatmi Abdeljalil , Daoudi Maria , Ben Larbi Najib , Kerbal Abdelali , Filali Baba Mohamed , El Bali Brahim , Bolte Michael , Mchich Mohamed , Ben-Hadda Taibi
Published: April 2009

The product 2 was prepared by the addition of piperazine (C4H10N2) to 1 [1] according to the reported procedure [2].[...]
Synthesis of 6-carbomethoxy-3-Phenyl-5-(4-dimethylaminophenyl)-cyclohexenone
Authors: Lobo Gricela , Charris Jaime
Published: April 2009

A mixture of 4-dimethylaminochalcone 1 (0.25 g, 1.00 mmol), methyl acetoacetate (0.17 g, 1.5 mmol) in methanol (5.00 mL) and sodium metoxide (0.25 mg) was stirred at room temperature for 24 hour to give a yellow precipitate.[...]
Synthesis of 8-chloro-11-(4-(3-(p-tolyloxy)propyl)piperazin-1-yl)-5H-dibenzo[b,e][1,4]diazepine
Authors: Capuano Ben , Crosby Ian T. , Lim Sean E. K. , Lloyd Edward J.
Published: April 2009

n/a
Ethyl 1-(4-chlorophenyl)-5,6-dimethyl-7,8a-diphenyl-4,5,6,8a-tetrahydro-1H-[1,2,4] triazolo[4,3-c][1,3]diazine-3-carboxylate
Authors: Boudina A. , Baouid A. , Hasnaoui A.
Published: April 2009

Compound 1 [1] (200 mg, 0.41 mmol) was refluxed in dimethylsulfoxide for 30 minutes.[...]
2-(Pyrazin-2-yliminomethyl)phenol
Authors: Asiri Abdullah Mohamed
Published: April 2009

Schiff bases from 2-hydroxy-1-naphthaldehyde have often been used as chelating ligands in the field coordination chemistry [1].[...]
Synthesis and Physical Characterization of 4-(anthracen-10-yl)-1-(4-mthoxyphenyl)-3-phenoxyazetidin-2-one as a New Cis 2-azetidinone
Authors: Jarrahpour Aliasghar , Nazari Mohammad , Jalbout Abraham
Published: April 2009

The synthesis of 4-(anthracen-10-yl)-1-(4-methoxyphenyl)-3-phenoxy azetidin-2-one is presented here. The AM1 calculations for characterizing the physical properties of the molecule are also given.
Microwave Induced Efficient Synthesis of 2-(1H-benzimidazol-2-ylthio)-4-methylquinoline
Authors: Raghavendra M. , Bhojya Naik Halehatty , Ravikumar Naik Tangali , Sherigara Bailure
Published: April 2009

Quinoline derivatives posses wide class of biological activities [1,2,3,4,5].[...]
3-tert-butoxycarbonylamino-pyridine-2-carboxylic Acid
Authors: Mamouni Rachid , El Haddad Mohammadine , Akssira Mohamed
Published: April 2009

To the carbamic acid tert-butylester 1 (1.03 g, 4.08 mmol) in methanol (15 ml) was added 1.4 equivalents of NaOH (2N).[...]
Synthesis of 4-bromo-2-thiomorpholin-4-ylmethyl-1-phenol
Authors: Velázquez Ana María , Torres Luis Alberto , González Raúl , Valencia Alvaro , Díaz-Barriga Sandra , Menconi Italo , Martínez Luisa , Ramírez Alberto , Martínez Ignacio , Camacho Brígida , López-Castañares Rafael , Angeles Enrique
Published: April 2009

4-bromo-2-thiomorpholin-4-ylmethyl-1-phenol (2) was prepared from 4-bromophenol (1) and thiomorpholine and formaldehyde (2 eq.) and 1 eq. of thiomorpholine.[...]
Synthesis of 4-isopropyl-bis-2,6-morpholin-4-ylmethyl-1-phenol
Authors: Velázquez A. Ma. , Torres L. , González R. , Valencia A. , Menconi L , Martínez L. , Ramírez A. , Camacho B. , Díaz-Barriga S. , López-Castañares R. , Angeles E.
Published: April 2009

4-isopropyl-bis-2,6-morpholin-4-ylmethyl-1-phenol (2) was prepared from 4-isopropylphenol (1) and formaldehyde (2 eq.) and 2 eq. of morpholine.[...]
2-[(2-Hydroxy-benzylidene)-amino]-5,6-dihydro-4H-cyclopenta [b] Thiophene-3-carboxylic Acid Methyl Ester
Authors: Asiri Abdullah Mohamed
Published: April 2009

Schiff bases from 2-hydroxy-1-naphthaldehyde have often been used as chelating ligands in the field coordination chemistry [1].[...]
Synthesis of 2-Fluoromethyl-7-methylnaphthalene
Authors: Bogdanov Jane , Maslak Przemyslaw
Published: April 2009

n/a
7-Hydroxy-8-acetylcoumarin N-1-(Carboxymethyl)pyridinium Chloride Hydrazone
Authors: Kotali Antigoni , Lafazanis Ioannis , Harris Philip
Published: April 2009

n/a
Synthesis and Characterization of N,N’-(propane-1,2 diyldicarbamothioyl)dibenzamide
Authors: Kurt Gülşah , Mercimek Bedrettin
Published: April 2009

Benzoylthioureas have found some interest due to their biological activity [1], spectroscopic and structural properties [2,3], or as synthetic building blocks [4].[...]
Phylogenetic analysis of sexual systems in Inuleae (Asteraceae)
Authors: Torices Rubén , Anderberg Arne A.
Published: April 2009

From an ancestor with bisexual flowers, plants with unisexual flowers, or even unisexual individuals have evolved in different lineages of angiosperms. The Asteraceae tribe Inuleae includes hermaphroditic, monoecious, dioecious, and gynomonoecious species. Gynomonoecy, the sexual system in which female and bisexual flowers occur on the same plant, is prevalent in the Asteraceae. We inferred one large gene phylogeny (ndhF) and two supertrees to investigate whether gynomonoecy was a stage in the evolution from hermaphroditism to monoecy. We identified transitions in sexual system evolution using the stochastic character mapping method. From gynomonoecious ancestors, both hermaphroditic and monoecious descendants have evolved. Gynomonoecy was not restricted to a stage in the evolution toward monoecy because the number of transitions and the rate of change from monoecy to gynomonoecy were much higher than the opposite. We also investigated one hypothesized association among female flowers and the development of a petaloid ray as an explanation of gynomonoecy maintenance in Asteraceae. We found that peripheral female flowers and petaloid rays were phylogenetically correlated. However, empirical evidence shows that a causal relationship between these traits is not clear.
Comparative Oxidative Stability of Fatty Acid Alkyl Esters by Accelerated Methods
Authors: Moser Bryan R.
Published: April 2009

Several fatty acid alkyl esters were subjected to accelerated methods of oxidation, including EN 14112 (Rancimat method) and pressurized differential scanning calorimetry (PDSC). Structural trends elucidated from both methods that improved oxidative stability included decreasing the number of double bonds, introduction of trans as opposed to cis unsaturation, location of unsaturation closer to the ester head group, and elimination of hydroxyl groups. Also noticed with EN 14112 was an improvement in oxidative stability when a larger ester head group was utilized. Methyl esters that contained ten or less carbons in the fatty acid backbone were unacceptable for analysis at 110 °C (EN 14112) due to excessive sample evaporation. With respect to PDSC, a correlation was noticed in which the oxidation onset temperature (OT) of saturated fatty esters increased with decreasing molecular weight (R2 0.7328). In the case of the monounsaturates, a very strong inverse correlation was detected between molecular weight and OT (R2 0.9988), which was in agreement with EN 14112. Lastly, a strong direct correlation (R2 0.8759) was elucidated between OT and oil stability index (OSI, EN 14112, 80 °C). The correlation was not as strong (R2 0.5852) between OSI obtained at 110 °C and OT.
In vivo non‐enzymatic repair of DNA oxidative damage by polyphenols
Authors: Tan Xiaorong , Zhao Chenyang , Pan Jing , Shi Yimin , Liu Guoan , Zhou Bo , Zheng Rongliang
Published: April 2009

The non‐enzymatic repair of DNA oxidative damage can occur in a purely chemical system, but data show that it might also occur in cells. Human hepatoma cells (SMMC‐7721) and human hepatocyte cells (LO2) were treated with 200 μM H2O2 for 30 min to induce oxidative DNA damage quantified by amount of 8‐OHdG and degree of DNA strand breaks, without inducing enzymatic repair. The dynamics of enzymatic repair activity quantified by unscheduled DNA synthesis, within 30 min after removal of H2O2 enzymatic repair mechanism has not been initiated. However, pre‐incubation with low micromolar level polyphenols, quercetin or rutin can significantly attenuate DNA damage in both cell lines, indicating that the polyphenols did not work through an enzymatic mechanism. Unscheduled DNA synthesis after removal of H2O2 was also markedly decreased by quercetin and rutin. Combined with our previous studies of fast reaction chemistry, the inhibitory effect of polyphenols have to be assigned to non‐enzymatic repair mechanism rather than to enzymatic repair mechanism or antioxidant mechanism.
Management of pediatric orbital cellulitis in patients with radiographic findings of subperiosteal abscess
Authors: Ryan Jesse T. , Preciado Diego A. , Bauman Nancy , Pena Maria , Bose Sumit , Zalzal George H. , Choi Sukgi
Published: April 2009

Objective

Controversies remain regarding the management of orbital cellulitis (OC). The objective of this study was to examine the outcomes of patients admitted to our institution for orbital cellulitis during a 7‐year period.

Study Design

Case series with chart review.

Setting

Tertiary referral pediatric hospital.

Subjects and Methods

Charts of 465 consecutive OC admissions were reviewed for presentation, imaging, medical and surgical treatment, and outcome.

Results

Of these patients, 189 were treated in the emergency room and 276 were admitted. CT scan was performed on 240 patients. Subperiosteal abscess (SPA) was noted in 68 patients. Of these, 47 were treated medically and 21 had surgery. Surgical patients were older (8.3 vs 6.2 years, P = 0.039), had larger abscesses (>10 mm, P < 0.001), required a longer admission (10.2 vs 6.6 days, P < 0.001), and had higher temperatures on admission (38.0°C vs 37.3°C, P = 0.03).

Conclusion

The majority of small SPAs as diagnosed on CT scans in younger children can be successfully treated medically. Surgery, however, should be considered for a worsening clinical examination. Our findings confirm those of previous reports on this clinical entity.
Fixed point theorems by altering distances between the points
Authors: Khan M.S. , Swaleh M. , Sessa S.
Published: April 2009

In this paper we have established some fixed point theorems in complete and compact metric spaces.
On a C–plane of order 25
Authors: Narayana Rao M.L. , Satyanarayana K.
Published: April 2009

Rao, Rodabaugh, Wilke and Zemmer [J. Combin. Theory Ser. A. 11 (1971), 72–92] constructed a number of new VW systems called C-systems from the exceptional near–fields and established that they coordinatize translation planes not isomorphic to generalized André planes. In this paper the translation complement of the plane coordinatized by the C-system I–1 has been found. This plane has the interesting property that its translation complement divides the ideal points into two orbits of lengths 10 and 16. Further, the translation complement contains a subgroup isomorphic to SL(2,5) and therefore one of the exceptional Walker's planes of order 25 [H. Luneberg, Translation Planes, Springer-Verlag (1980), pp.235–244] is indeed the C–plane corresponding to the C–system I–1, which was discovered in 1969.
On p–valent starlike functions with reference to the Bernardi integral operator
Authors: Kumar Vinod , Shukla S.L.
Published: April 2009

Let (A, B) denote the class of certain p-valent starlike functions. Recently G. Lakshma Reddy and K.S. Padmanabhan [Bull. Austral. Math. Soc. 25 (1982), 387–396] have shown that the function g defined by

belongs to the class (A, B) if f ∈ (A, B). The technique used by them fails when c is any positive real number. In this paper, by employing a more powerful technique, we improve their result to the case when c is any real number such that c ≥ −p(1+A)/(1+B).
Central commutators
Authors: Caranti A. , Scoppola C.M.
Published: April 2009

We give examples of finite groups of odd prime power order in which the commutators lying in the centre do not generate the intersection of the centre and the commutator subgroup.
Periodic solutions of the boundary value problem for the nonlinear heat equation
Authors: Nkashama M. N. , Willem M.
Published: April 2009

We prove the existence of generalized periodic solutions of the boundary value problem for the nonlinear heat equation. The proof is based on classical Leray-Schauder's techniques and coincidence degree.
On a problem of Favard concerning algebraic integers
Authors: Lloyd-Smith C. W.
Published: April 2009

Let α be an algebraic integer of degree n > 1 with conjugates α = α1, α2, …, αn. Let D(α) denote the diameter of {α1, …, αn} and diam . In 1929 Favard showed that diam and that, when n = 2 or 3, the minimal values of diam (α) are less than 2. The author shows that diam and He also finds all algebraic integers a with diam (α) ≤ 2 when n ≤ 5. Similar results are found for D(α) and, in particular, D(α) > 2 when n = 5.
Almost complex structures on four-dimensional complete intersections
Authors: Hiller Howard
Published: April 2009

Suppose X is a 4-dimensional complete intersection in CPr+4 of multidegree d1, …, dr. We show that X supports infinitely many almost complex structures for exactly 8 possible multi-degrees. In particular, a hypersurface of degree d in CP5 admits infinitely many almost complex structures if and only if d = 2 or 6. This generalizes a result of E. Thomas [4] for CP4. We give also some tables of possible Todd genera and a result for complex surfaces.
Nemitsky operators between Orlicz-Sobolev spaces
Authors: Hardy Grahame
Published: April 2009

A theorem on Nemitsky operators between Sobolev spaces, contained in a 1973 paper of Marcus and Mizel, is extended to Orlicz-Sobolev spaces.
Compressible matrix rings
Authors: Armendariz Efraim P. , Park Jae Keol
Published: April 2009

Let Z(K) denote the center of a ring K. A ring R is compressible if Z(eRe) = eZ(R) for each idempotent e of R. In response to a question of S. Berberian, G. Bergman has constructed a (non-commutative) integral domain, satisfying a polynomial identity, for which the 2×2 matrix ring over the domain is not compressible. In contrast to Bergman's example, we show that the ring of nxn matrices over any commutative ring is always compressible.
An effective seven cube theorem
Authors: Cook R. J.
Published: April 2009

It is well-known that every sufficiently large positive integer is the sum of seven cubes. Both proofs of this result, due to Linnik and Watson, are ineffective. Here we show that Watson's proof may be made effective.
Meromorphic starlike univalent functions
Authors: Anh V. V. , Tuan P. D.
Published: April 2009

Let B be the class of functions ω(z) regular in |z| < 1 and satisfying ω(0) = 0, |ω(z)|<1 in |z|<1. We denote by P(A, B), −1 ≤ B < A ≤1, the class of functions p(z) = l+p1z+… regular in |z| < 1 and such that p(z) = [1+Aω(z)]/[1+Bω(z)] for some ω(z) ∈ Β. This paper establishes sharp lower and upper bounds on |z| = r<1 for the functional

where p(z) varies in P(A, B). The results are then used to study certain geometric properties of the corresponding class of meromorphic starlike univalent functions
Length and area inequalities for the derivative of a bounded and holomorphic function
Authors: Yamashita Shinji
Published: April 2009

The Schwarz-Pick lemma,

for f analytic and bounded, |f|<1, in the disk |z|<1, is refined:

where Φ(z, r) is a quantity determined by the non-Euclidean area of the image of

and ψ(z, r) is that determined by the non-Euclidean length of the image of the boundary of D(z, r). The multiplicities in both images by f are not counted.
Topological categories with many symmetric monoidal closed structures
Authors: Kelly G.M. , Rossi F.
Published: April 2009

It would seem from results of Foltz, Lair, and Kelly that symmetric monoidal closed structures, and even monoidal biclosed ones, are quite rare on one-sorted algebraic or essentially-algebraic categories. They showed many such categories to admit no such structures at all, and others to admit only one or two; no such category is known to admit an infinite set of such structures.

Among concrete categories, topological ones are in some sense at the other extreme from essentially-algebraic ones; and one is led to ask whether a topological category may admit many such structures. On the category of topological spaces itself, only one such structure - in fact symmetric - is known; although Greve has shown it to admit a proper class of monoidal closed structures. One of our main results is a proof that none of these structures described by Greve, except the classical one, is biclosed.

Our other main result is that, nevertheless, there exist topological categories (of quasi-topological spaces) which admit a proper class of symmetric monoidal closed structures. Even if we insist (like most authors) that topological categories must be wellpowered, we can still exhibit ones with more such structures than any small cardinal.
A geometrically aberrant Banach space with normal structure
Authors: Giles J.R. , Sims Brailey , Swaminathan S.
Published: April 2009

An example is given of a Banach space with normal structure which does not satisfy the geometrical conditions commonly expected to be related to normal structure.
Weighted composition operators on functional Hilbert spaces
Authors: Singh R.K. , Chandra Kumar R. David
Published: April 2009

Let X be a non-empty set and let H(X) denote a Hibert space of complex-valued functions on X. Let T be a mapping from X to X and θ a mapping from X to C such that for all f in H(X), f ° T is in H(x) and the mappings CT taking f to f ° T and M taking f to θ.f are bounded linear operators on H(X). Then the operator CTMθ is called a weighted composition operator on H(X). This note is a report on the characterization of weighted composition operators on functional Hilbert spaces and the computation of the adjoint of such operators on L2 of an atomic measure space. Also the Fredholm criteria are discussed for such classes of operators.
On the volume and projection of convex sets containing no lattice points
Authors: Scott P. R.
Published: April 2009

A convex body K in En containing no lattice points, has one-deimensional projections of lengths X1, X2, …, Xn on the coordinate axes. We show that for n ≥ 2 and 1 ≤ Xi ≤ n/(n−1) (1 ≤ i ≤ n),

and this bound can not be improved.
Essential completions of distributive lattices
Authors: Gierz Gerhard , Stralka Albert R.
Published: April 2009

The salient feature of the essential completion process is that for most common distributive lattices it will yield a completely distributive lattice. In this note it is shown that for those distributive lattices which have at least one completely distributive essential extension the essential completion is minimal among the completions by infinitely distributive lattices. Thus in its setting the essential completion of a distributive lattice behaves in much the some way as the one-point compactification of locally compact topological space does in its setting.
Derivations on commutative operator algebras
Authors: Spivack Mark
Published: April 2009

It is well-known that any derivation on a commutative von Neumann algebra is implemented by a bounded operator. In this note we present a simple alternative proof, which generalizes the result further within Hilbert space, and to reflexive Banach spaces.
Some recent results for heat-diffusion moving boundary problems
Authors: Hall James M. , Dewynne Jeffrey N.
Published: April 2009

Integral formulations for the three classical single phase Stefan problems involving the infinite slab and inward solidifying cylinders and spheres are utilized to generate standard analytical approximations. These approximations include the pseudo steady state estimate, large Stefan number expansions, upper and lower bounds, approximations based on integral iteration and related results such as formal series solutions. In order to demonstrate the applicability and limitations of the integral formulations three generalizations of the classical stefan problem are considered briefly. These problems are diffusion with two simultaneous chemical reactions, a Stefan problem with two moving boundaries and the genuine two phase Stefan problem.
Epicomplete archimedean lattice-ordered groups
Authors: Ton Dao-Rong
Published: April 2009

In this paper we give the structure of an ℵi-complete ℓ-group and the epicomplete objects in the categoryAℓ.
Elementary observations on 2-categorical limits
Authors: Kelly G.M.
Published: April 2009

With a view to further applications, we give a self-contained account of indexed limits for 2-categories, including necessary and sufficient conditions for 2-categorical completeness. Many important 2-categories fail to be complete but do admit a wide class of limits. Accordingly, we introduce a variety of particular 2-categorical limits of practical importance, and show that certain of these suffice for the existence of indexed lax- and pseudo-limits. Other important 2-categories fail to admit even pseudo-limits, but do admit the weaker bilimits; we end by discussing these.
A simple proof of the Erdos-Gallai theorem on graph sequences
Authors: Choudum S.A.
Published: April 2009

A central theorem in the theory of graphic sequences is due to P. Erdos and T. Gallai. Here, we give a simple proof of this theorem by induction on the sum of the sequence.
Torsion in the additive group of relatively free Lie rings
Authors: Drensky Vesselin
Published: April 2009

Let L = L(X) be the free Lie ring of countable rank and let p be prime. Then L(Vp) = L/[(L')p, L] is the relatively free ring for the variety of Lie rings Vp = [Np−1A, E] and Vp is defined by the identity

The purpose of this note is to establish that there exist elements of order p in the additive group of L(Vp). Previously, the existence of p-torsion was proved by Kuz'min for p = 2 only. Similar results were obtained for varieties of groups by Gupta when p = 2 and by Stöhr when p = 3.
An asymptotic theorem for abstract differential equations
Authors: N'Guérékata Gaston Mandata
Published: April 2009

In this paper, we prove the existence of a continuous one-to-one correspondence between bounded solutions of the equation x′(t) = Ax(t) + b(t) which belong to a certain subclass L+ of and bounded mild solutions of the equation x′(t) = Ax(t) + b(t) + f(t, x(t)) of the form u(t) = ø(t) + Ψ(t), with ø(t) ∈ L+ and .
Fields countably generated over a proper subfield
Authors: Deveney James K. , Yanik Joe
Published: April 2009

For an arbitrary field K there are two related questions that can be asked:

(1) Is there a proper subfield, L, of K such that K is countably generated over L?

(2) Given a proper subfield M of K is there a proper subfield, L, of K containing M such that K is countably generated over L?

We give an affirmative answer to (1) in characteristic p ≠ 0 and provide counterexamples to (2) for arbitrary characteristic ≠ 2.
Subdirect decompositions of the lattice of varieties of completely regular semigroups
Authors: Trotter P.G.
Published: April 2009

It is shown that if V is an element of the lattice of the title then the map given by U → (V ∧ U, V ∨ U) is a complete lattice embedding of into (V] × [V) if and only if V is a join-infinitely distributive element. In this case the image of the map is a subdirect product of the principal ideal (V] by the principal filter [V) generated by V. Some important varieties in are shown to be join-infinitely distributive.
Idempotents in bicategories
Authors: Paré R. , Rosebrugh R. , Wood R.J.
Published: April 2009

It is shown that the category of fixed points of a left exact idempotent functor on a topos is again a topos. As well as a direct proof, a bicategorical proof is given which shows that the result only depends on certain bicategorical exactness properties.
Local boundedness of monotone operators under minimal hypotheses
Authors: Borwein Jon , Fitzpatrick Simon
Published: April 2009

We give a short proof the local boundedness of a monotone operator as an easy consequence of the continuity of an associated convex function.
On the twice differentiability of viscosity solutions of nonlinear elliptic equations
Authors: Trudinger Neil S.
Published: April 2009

We prove, under very general structure conditions, that continuous viscosity subsolutions of nonlinear second-order elliptic equations possess second order superdifferentials almost everywhere. Consequently we deduce the twice differentiability almost everywhere of viscosity solutions. The main idea of the proof is the backwards use of the Aleksandrov maximum principle as invoked in a previous work of Nadirashvili on sequences of solutions of linear elliptic equations.
Strongly Right Fbn Rings: Corrigendum
Authors: Lee Heakyung
Published: April 2009

The author would like to include some information omitted from the paper by a publishing error.

The paragraph following Lemma 2.1 on page 458.
Non commutative convolution measure algebras with no proper L-ideals
Authors: Albar Sahl Fadul
Published: April 2009

We study non-commutative convolution measure algebras satisfying the condition in the title and having an involution with a non-degenerate finite dimensional *-representation. We show first that the group algebra L1(G) of a locally compact group G satisfies these conditions. Then we show that to a given algebra A with the above conditions there corresponds a locally compact group G such that A is a * and L-subalgebra of M(G) and such that the enveloping C*-algebra of A is *isomorphic to C*(G). Finally we show for certain groups that L1(G) is the only example of such algebras, thus giving a characterisation of L1(G).
Decay estimates for some nonlinear second order ordinary differential equations
Authors: Nakao Mitsuhiro
Published: April 2009

Precise decay estimates as t → ∞ are derived for a class of nonlinear second order ordinary differential equations of the form

where h, g and f are functions like

With α > −1, β > −1 and γ > −1.
Bounded measurable simultaneous monotone approximation
Authors: Sahab Salem M.A.
Published: April 2009

Let X = [a, b] be a closed bounded real interval. Let B be the closed linear space of all bounded real valued functions defined on X, and let M ⊆ B be the closed convex cone consisting of all monotone non-decreasing functions on X. For f, g ∈ B and a fixed positive w ∈ B, we define the so-called best L∞-simultaneous approximant of f and g to be an element h* ∈ M satisfying

for all h ∈ M, where

We establish a duality result involving the value of d in terms of f, g and w only.

If in addition f, g and w are continuous, then some characterisation results are obtained.
Identities for existence varieties of regular semigroups
Authors: Hall T.E.
Published: April 2009

A natural concept of variety for regular semigroups is introduced: an existence variety (or e-variety) of regular semigroups is a class of regular semigroups closed under the operations H, Se, P of taking all homomorphic images, regular subsernigroups and direct products respectively. Examples include the class of orthodox semigroups, the class of (regular) locally inverse semigroups and the class of regular E-solid semigroups. The lattice of e-varieties of regular semigroups includes the lattices of varieties of inverse semigroups and of completely regular semigroups. A Birkhoff-type theorem is proved, showing that each e-variety is determined by a set of identities: such identities are then given for many e-varieties. The concept is meaningful in universal algebra, and as for regular semigroups could give interesting results for e-varieties of regular rings.
A note on connected submetaLindelöf spaces
Authors: Kemoto Nobuyuki
Published: April 2009

In this paper, we shall show that if m is a natural number and for every 0 ≦ n ≦ m, and 2ω ≦ ωm are assumed, then connected, locally Lindelöf, submetaLindelöf, normal spaces of character ≦ 2ω are Lindelöf. Furthermore, we shall show that if and only if connected, locally Lindelöf, submetaLindelöf, normal spaces of character ≦ 2ω and tightness ≦ ω are Lindelöf.
Approximating fixed points by ishikawa iterates
Authors: Maiti M. , Ghosh M.K.
Published: April 2009

In a uniformly convex Banach space the convergence of Ishikawa iterates to a fixed point is discussed for nonexpansive and generalised nonexpansive mappings.
Generalised Hölderian functions
Authors: De Sarkar S. , Panda S.
Published: April 2009

The concept of kth Hölderian functions on an interval [a, b] which generalises the notion of Hölderian (Lipschitzian) functions of positive order on [a, b] is introduced. The relationship of such functions to functions of bounded kth variation and absolutely kth continuous functions is examined. Properties induced by higher order derivatives in this new class of functions are investigated.
On the Kneser-Hukuhara property for integral equations in locally convex spaces
Authors: Szufla Stanislaw
Published: April 2009

This paper contains a Hukuhara – type theorem for nonlinear Volterra integral equations in locally convex spaces.
How complete are categories of algebras?
Authors: Adámek Jiří
Published: April 2009

Completeness properties of (i) the category Alg(T) of T-algebras over a functor T: X → X and (ii) the subcategory XT in the case where T = (T, μ, η) is a monad, are investigated. It is known that if X is compact, then each XT is compact; we present a functor T: Set → Set such that Alg(T) is non-compact, although it is hypercomplete. If T either preserves epis or has a rank, we prove that Alg(T) and XT are topologically algebraic over X provided X satisfies mild additional hypotheses. Nevertheless, a natural monad over the category of Δ-comp1ete posets is exhibited such that its category of algebras is solid, but not topologically algebraic, over Set.
There are no chaotic mappings with residual scrambled sets
Authors: Gedeon T.
Published: April 2009

A continuous mapping f of a compact real interval I to itself which is chaotic in the sense of Li and Yorke, cannot have a scrambled set residual in an subinterval of I. This shows that chaos in this case cannot be large from a topological point of view.
On maximum matchings in cubic graphs with a bounded number of bridge-covering paths
Authors: Chartrand Gary , Kapoor S.F. , Oellermann Ortrud R. , Ruiz Sergio
Published: April 2009

It is proved that if G is a connected cubic graph of order p all of whose bridges lie on r edge-disjoint paths of G, then every maximum matching of G contains at least P/2 − └2r/3┘ edges. Moreover, this result is shown to be best possible.
Modular fitting functors in finite groups
Authors: Hauck Peter , Kienzle Reinhold
Published: April 2009

We consider Fitting classes for which the injectors in any finite solvable group are modular subgroups. It is shown that only normal Fitting classes have this property. In fact, we prove two more general results demonstrating that modular Fitting functors and submodular Fitting classes are normal.
A note on additive mappings in noncommutative fields
Authors: Vukman J.
Published: April 2009

In this paper we prove a result concerning the Cauchy functional equation, that is the functional equation f(x + y) = f(x) + f(y), in skew fields with characteristic not two.
A family of balanced ternary designs with block size four
Authors: Donovan Diane
Published: April 2009

This paper shows the existence of an infinite family of cyclic balanced ternary designs where the block size is 4, the index 2 and each block contains precisely one repeated element.
Laurent expansion of Dirichlet series
Authors: Balakrishnan U.
Published: April 2009

Let 〈an〉 be an increasing sequence of real numbers and 〈bn a sequence of positive real numbers. We deal here with the Dirichlet series and its Laurent expansion at the abscissa of convergence, λ, say. When an and bn behave like

as N → ∞, where P2(x) is a certain polynomial, we obtain the Laurent expansion of f (s) at s = λ, namely

where P1(x) is a polynomial connected with P2(x) above. Also, the connection between P1 and P2 is made intuitively transparent in the proof.
On weak convergence implying strong convergence in L1-spaces
Authors: Balder Erik J.
Published: April 2009

Recently, Visintin gave conditions under which weak convergence in L1 (T;RN) implies strong convergence. Here we analyze such results in terms of associated young measures and present an extension to L1 (T;Ξ), where Ξ is a separable reflexive Banach space.
A coincidence theorem in topological vector spaces
Authors: Hadžić Olga
Published: April 2009

In this paper we prove a coincidence theorem in not necessarily locally convex topological vector spaces, which contains, as a special case, a coincidence theorem proved by Felix Browder. As an application, a result about the existence of maximal elements is obtained.
Elementary equivalence and genus of finitely generated nilpotent groups
Authors: Oger Francis
Published: April 2009

We show that, if two finitely generated nilpotent groups are elementarily equivalent, and more generally if they satisfy the same sentences with one alternation of quantifiers, then, they are quite similar, though not necessarily isomorphic. For instance, each of them is isomorphic to a subgroup of finite index of the other and they have the same finite images, the same Mislin genus and the same Pickel genus.
Projective tensor products and the Dunford–Pettis property
Authors: Stehle Stephen P.
Published: April 2009

We show the existence, in c0 ⊗γc0, of a shrinking, subsymmetric basic sequence (zi) having no c0 subsequences. In particular, the coefficient functionals for (zi) are weakly null and the subspace fails to have the Dunford-Pettis property.
Some groups all of whose proper verbal quotients are relatively free
Authors: Higman Graham
Published: April 2009

A class of blocking pairs (A, B) for which B/AB is infinite cyclic is constructed and these are used to construct groups all of whose proper verbal quotients are relatively free.
Free Fibonacci algebras
Authors: Jonnson D.L. , Kim A.C.
Published: April 2009

Fibonacci varieties were introduced by one of us in 1978 and a natural generalisation was studied shortly afterwards. We carry this investigation one stage further by giving a description of the free objects in these varieties. This is done in terms of the n-abelian groups of Levi.
Wreath decompositions of finite permutation groups
Authors: Kovács L. G.
Published: April 2009

There is a familiar construction with two finite, transitive permutation groups as input and a finite, transitive permutation group, called their wreath product, as output. The corresponding ‘imprimitive wreath decomposition’ concept is the first subject of this paper. A formal definition is adopted and an overview obtained for all such decompositions of any given finite, transitive group. The result may be heuristically expressed as follows, exploiting the associative nature of the construction. Each finite transitive permutation group may be written, essentially uniquely, as the wreath product of a sequence of wreath-indecomposable groups, amid the two-factor wreath decompositions of the group are precisely those which one obtains by bracketing this many-factor decomposition.

If both input groups are nontrivial, the output above is always imprimitive. A similar construction gives a primitive output, called the wreath product in product action, provided the first input group is primitive and not regular. The second subject of the paper is the ‘product action wreath decomposition’ concept dual to this. An analogue of the result stated above is established for primitive groups with nonabelian socle.

Given a primitive subgroup G with non-regular socle in some symmetric group S, how many subgroups W of S which contain G and have the same socle, are wreath products in product action? The third part of the paper outlines an algorithm which reduces this count to questions about permutation groups whose degrees are very much smaller than that of G.
Some remarks on the computation of conjugacy classes of soluble groups
Authors: Mecky M. , Neubüser J.
Published: April 2009

Laue et al have described basic algorithms for computing in a finite soluble group G given by an AG-presentation, among them a general algorithm for the computation of the orbits of such a group acting on some set Ω. Among other applications, this algorithm yields straightforwardly a method for the computation of the conjugacy classes of elements in such a group, which has been implemented in 1986 in FORTRAN within SOGOS by the first author and in 1987 in C within CAYLEY. However, for this particular problem one can do better, as discussed in this note.
On the date of Cauchy's contributions to the founding of the theory of groups
Authors: Neumann Peter M.
Published: April 2009

Evidence front published sources is used to show that Cauchy's group-theoretical work was all produced in a few months of intense activity starting in September 1845.
Asymptotically stable attracting sets in the Navier-Stokes equations
Authors: Kloeden P. E.
Published: April 2009

The planar Navier-Stokes equations with periodic boundary conditions are shown to have a nearby asymptotically stable attracting set whenever a Galerkin approximation involving the eigenfunctions of the Stokes operator has such an attracting set, provided the approximation has sufficiently many terms and its attracting set is sufficiently strongly stable. Lyapunov functions are used to characterize the stability of these attracting sets, which are compact sets of arbitrary geometric shape. This generalizes earlier results of Constantin, Foias and Temam and of the author for asymptotically stable steady solutions in the Navier-Stokes equations and such Galerkin approximations.
A test function theorem and apporoximation by pseudopolynomials
Authors: Badea C. , Badea I. , Gonska H. H.
Published: April 2009

We prove a Korovkin-type theorem on approximation of bivariate functions in the space ofB-continuous functions (introduced by K. Bögel in 1934). As consequences, some sequences of uniformly approximating pseudopolynomials are obtained.
On the decomposition of integral lattices
Authors: Bier Thomas
Published: April 2009

The purpose of this note is to record a few formulas relating the indices of various lattices and sublattices all arising from the decomposition of a euclidean space E into three mutually orthogonal subspaces E = E0 ⊥ E1 ⊥ E2 which are rational with respect to a given lattice Λ ⊂ E. In the case that Λ is unimodular these formulas simplify to give very simple identities between various intersection lattices.
Convex sets, fixed points, variational and minimax inequalities
Authors: Lin Tzu-Chu
Published: April 2009

Recently, Ky Fan extended his will known lemma (which is an extension of the classical theorem of Knaster, Kuratowski and Mazurkiewica) to the noncompact case. Using this result, another interesting lemma of Fan is generalized in this paper. As applications of our theorem, we obtain a generalizationof Browder's variational inequality and derive Fan's other recent results directly from our theorem. Also, in this paper, we give a slight extension recent results of K. K. Tan, which themselves are generalizations of many well-known results on minimax and variational inequalities.
On Convergence theorems for nonabsolute integrals
Authors: Yee Lee Peng , Seng Chew Tuan
Published: April 2009

In this paper the Perron integrability of the limit of a sequence of functions is proved under certain convergene conditions.
Existence of an order-preserving function on normally preordered spaces
Authors: Mehta Ghanshyam
Published: April 2009

The object of this paper is to generalize the classic theorems of Eilenberg and Debreu on the existence of continuous order-preserving transformations on ordered topological spaces and to prove them in a different way. The proof of the theorems is based on Nachbin's generalization to ordered topological spaces of Urysohn's separation theorem in normal topological spaces.
On a centre-like subset of a ring without nil ideals
Authors: Nada Itzhak
Published: April 2009

We give a new proof of the hypercentre theorem of Herstein.

In [1], Herstein has defined the hypercentre of a ring R as follows:

Herstein has proved:

THEOREM. If R is a ring without non-zero nil ideals, thenT (R) = Z (R).
A generalization of Radon's theorem II
Authors: Tverberg H.
Published: April 2009

A new proof is given of the following result: Let m and d be positive integers, and let a set of md + m − d points be given in d-dimensional space. Then the set can be partitioned into m sets such that the m convex polytopes spanned by the sets have a non-empty intersection.
Necessary and sufficient conditions for spectral sets
Authors: Furuta Takayuki , Chō Muneo
Published: April 2009

We shall show necessary and sufficient conditions for which closed setXin the complex plane is a spectral set of an operatorTon a complex Hilbert space.
Manufacturing sequences for the Economic Lot Scheduling problem
Authors: Fitz-Gerald James M. , Billington Elizabeth J.
Published: April 2009

In the basic Economic Lot Scheduling problem, a production schedule is required to manufacture sequentially a number of products on a single machine, with the schedule chosen to minimize set-up and inventory costs. The products suffer continuous demand, and no shortfall is allowed. A recent approach involves repetitions of a production cycle (such as ABCBC for three products A, B and C, with manufacturing times chosen to prevent shortage occurring); an exhaustive search is performed over a large set of possible cycles to discover the optimal schedule.

This paper discusses the question “How many such sycles need to be examined?”, Since the answer is very relevant to practical application of the method. The case of three products is considered. Complete information is obtained for cycles up to length 12 (that is, 12 production switch overs), and partial results for longer ones. An estimate, apparently reasonable, is obtained for cycles of any length. The major trend to emerge is that surprisingly few cycles are involved.
Iteration of piecewise linear maps on an interval
Authors: McGuire James B. , Thompson Colin J.
Published: April 2009

A complete analysis is given of the iterative properties of two piece-piecewise linear maps on an interval, from the point of view of a doubling transformation obtained by functional composition and rescaling. We show how invariant measures may be constructed for such maps and that parameter values where this may be done form a dense set in a one-dimensional subset of parameter space.
Topologies induced by metrics with disconnected range
Authors: Broughan Kevin
Published: April 2009

In a metric space (X, d) a ball B(x, ε) is separated if d(B(x, ε), X\B(x, ε)] > 0. If the separated balls form a sub-base for the d-topology then Ind X = 0. The metric is gap-like at x if dx(X) is not dense in any neighbourhood of 0 in [0, ∞). The usual metric on the irrational numbers, P, is the uniform limit of compatible metrics (dn), each dn being gap-like on P. In a completely metrizable space X if each dense Gδ is an Fσ then Ind X = 0.
Localization of patai's theorem on alephs
Authors: Bagemihl Frederick
Published: April 2009

If μ and γ are ordinal numbers such that for every α ≤ γ·2, then γ < ω. This localizes a result due to Patai.
The product of pre-Radon measures
Authors: Okada Susumu
Published: April 2009

Let μ and ν be non-σ-finite pre-Radon measures on topological spaces X and Y respectively. Then there exists a unique pre-Radon measure λ on the product space X × Y which satisfies λ(A × B) = μ(A)ν(B) for all Borel sets A in X and B in Y such that μ(A) < ∞ and ν(B) < ∞.
A note on 1-factors of point determining graphs
Authors: Gek-Ling Chia , Chong-Keang Lim
Published: April 2009

A graph is called point determining if distinct points have distinct neighborhoods. In this note we provide a sufficient condition for a point determining graph to have a 1-factor. This is an extension of some results obtained by David P. Sumner.
Infinite series and the derived set of the aggregate of the fractional parts of its partial sums: Addendum
Authors: Moorthy S. Audinarayana
Published: April 2009

In the author's paper [7] it was proved that the fractional parts of the partial sums of an infinite series (of real terms) diverging to +∞ or −∞, in which the general term tends to zero, are everywhere dense in the closed unit interval. This result was extended to series of infinite oscillation (see Remark 4.1 of the said paper) on the argument that a sequence of partial sums having infinite oscillation has a subsequence that diverges to +∞ or −∞.
On a 2-knot group with nontrivial center
Authors: Yoshikawa Katsuyuki
Published: April 2009

Jonathan A. Hillman asked “Must a 2-knot whose group has non-trivial center be fibered?” We will answer this question negatively.
Clique coverings of graphs V: maximal-clique partitions
Authors: Pullman N.J. , Shank H. , Wallis W.D.
Published: April 2009

A maximal-clique partition of a graph G is a way of covering G with maximal complete subgraphs, such that every edge belongs to exactly one of the subgraphs. If G has a maximal-clique partition, the maximal-clique partition number of G is the smallest cardinality of such partitions. In this paper the existence of maximal-clique partitions is discussed – for example, we explicitly describe all graphs with maximal degree at most four which have maximal-clique partitions - and discuss the maximal-clique partition number and its relationship to other clique covering and partition numbers. The number of different maximal-clique partitions of a given graph is also discussed. Several open problems are presented.
On analytic functions with reference to the Bernardi integral operator
Authors: Reddy G. Lakshma , Padmanabhan K.S.
Published: April 2009

Bernardi has proved that if f if starlike univalent in the uni disc E, then so is the function g given by

In the first part of the paper, we extend Bernardi's theorem to a certain class of p-valent starlike functions in E. We prove that if then g, defined by

also belongs to . In the second part of the paper we examine the converse problem for functions with negative coefficients, satisfying certain conditions.