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The notions of k-regularity and intra k-regularity in bi-semimodules of a Morita context of semirings have been introduced. Some characterizations of k-regular and intra kregular idempotent bi-semimodules of a Morita context of semirings have been obtained in terms of k-b-subsemimodules. Then the study of the interplay among various components of a Morita context of semirings in terms of k-regularity and intra k-regularity has been accomplished. Finally it has been shown that k-regularity and intra k-regularity are Morita invariant properties. [ABSTRACT FROM AUTHOR]

This paper considers the stability of a one-dimensional system during a catastrophic shift described by the Hill function. Because the shifting process goes through a nonequilibrium region, we applied the theory of Kosambi, Cartan, and Chern (KCC) to analyze the stability of this region based on the differential geometrical invariants of the system. Our results show that the Douglas tensor, one of the invariants in the KCC theory, affects the robustness of the trajectory during a catastrophic shift. In this analysis, the forward and backward shifts can have different Jacobi stability structures in the nonequilibrium region. Moreover, the bifurcation curve of the catastrophic shift can be interpreted geometrically, as the solution curve where the nonlinear connection and the deviation curvature become zero. KCC analysis also shows that even if the catastrophic pattern itself is similar, the stability structure in the nonequilibrium region is different in some cases, from the viewpoint of the Douglas tensor. [ABSTRACT FROM AUTHOR]

The theory of Cosserat rods provides versatile models to simulate large spatial deformations of slender flexible structures. As the strain measures of the mechanical theory are given in terms of the differential invariants of Cosserat curves, the kinematics of Cosserat rods is closely related to the differential geometry of framed curves. We utilize ideas from the difference geometry of framed curves in Euclidean space to construct the discrete kinematics of Cosserat rod models on a staggered grid, preserving the essential geometric properties independent of the coarseness of the discretization. [ABSTRACT FROM AUTHOR]

This study focused on the concept of arc length and curvature, being affine differential invariants of a curve in the plane. The Lie transformation groups theory implementing affine differential geometry was associated with these concepts in order to obtain the invariants by means of group operators. [ABSTRACT FROM AUTHOR]

This paper contains a weak lifting result for differential graded (DG) modules that is a generalization of Auslander, Ding, and Solberg's weak lifting for modules and Yoshino's weak lifting for complexes. [ABSTRACT FROM AUTHOR]

We prove new kinematic formulasfor tensor valuations and simplify previously known Crofton formulas by using therecently developed algebraic theory of translation invariant valuations. The heart of the paper is thecomputation of the Alesker–Fourier transform on the large class of spherical valuations, which is achieved by differential-geometric andrepresentation theoretical tools. We also describe in explicit form the product and convolution of tensor valuations. [ABSTRACT FROM AUTHOR]

As a unitary quantum walk with infinitely many internal degrees of freedom, the quantum walk in terms of quantum Bernoulli noise (recently introduced by Wang and Ye) shows a rather classical asymptotic behavior, which is quite different from the case of the usual quantum walks with a finite number of internal degrees of freedom. In this paper, we further examine the structure of the walk. By using the Fourier transform on the state space of the walk, we obtain a formula that links the moments of the walk’s probability distributions directly with annihilation and creation operators on Bernoulli functionals. We also prove some other results on the structure of the walk. Finally, as an application of these results, we establish a quantum central limit theorem for the annihilation and creation operators themselves. [ABSTRACT FROM AUTHOR]

We consider a vector bundle E → M and the principal bundle PE of frames of E. We determine all natural transformations of the connection bundle of the first order principal prolongation of principal bundle PE into itself. [ABSTRACT FROM AUTHOR]

This paper reconsiders scale-theoretical ideas from the standpoint of voice leading. I begin by showing that Clough and Douthett's definition of ‘maximal evenness’ makes covert reference to voice-leading distances, albeit disguised by the form of their equations. I then argue that theirs is a special case of the broader problem of quantizing continuous chords to a scale, deriving some new results in this more general setting – including an analogue of the ‘cardinality equals variety’ property. In the second part of the paper, I show how Clough and Douthett's ‘J-function’ began as a device for generating maximally even collections, only later evolving into a tool for studying the voice leadings between them. Particularly important here are Julian Hook's ‘signature transformations’, which I generalize to a wider range of collections. I conclude with a few remarks about history and methodology in music theory. [ABSTRACT FROM PUBLISHER]

Probabilistic quantum cloning (PQC) cannot copy a set of linearly dependent quantum states. In this paper, we show that if incorrect copies are allowed to be produced, linearly dependent quantum states may also be cloned by the PQC. By exploiting this kind of PQC to clone a special set of three linearly dependent quantum states, we derive the upper bound of the maximum confidence measure of a set. An explicit transformation of the maximum confidence measure is presented. [ABSTRACT FROM AUTHOR]

Applying Cartan's method of equivalence, this study demonstrates a classification of spacetime curves under Galilean motions. Among with trying to signify fundamental invariants which tend to new conservation laws, we also attempt to find a necessary and sufficient condition for Galilean equivalent curves via a simple and direct method. An straight forward deduction of our investigation in physics is, in addition, discussed. [ABSTRACT FROM AUTHOR]

We define and study the properties of a notion of morphism of enriched categories, intermediate between strong functor and profunctor. Suggested by bicategorical considerations, it turns out to be a generalization of Mealy machine, well-known since the 1950's in the theory of computation. When the base category is closed we construct a classifying category for Mealy morphisms, as we call them. This is also seen to give the free tensor completion of an enriched category. [ABSTRACT FROM AUTHOR]

We define the p-power quasiconcave function and show relationships between p-power quasiconcave fundamental function and r.i. spaces like Lorentz space and Marcinkiewicz space. [ABSTRACT FROM AUTHOR]

We discuss a model for quantum computing with initially mixed states. Although such a computer is known to be less powerful than a quantum computer operating with pure (entangled) states, it may efficiently solve some problems for which no efficient classical algorithms are known. We suggest a new implementation of quantum computation with initially mixed states in which an algorithm realization is achieved by means of optimal basis independent transformations of qubits. [ABSTRACT FROM AUTHOR]

By using the limiting case of Watson's q-Whipple transformation as n → ∞, we investigate the transformations of the nonterminating q-Kampé-de-Fériet series. Further, new formulas for the transformations and well-posed reduction formulas are established for the basic Clausen hypergeometric series. Several remarkable formulas are also found for new function classes beyond the q-Kampé-de-Fériet function. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, it is shown that Siler cones and of positive semidefinite-preserving linear transformations are equal. In the process of showing this, a common characterization theorem is given. [ABSTRACT FROM AUTHOR]

We construct a class of noninjective aperiodic circle transformations. As a by-product, we establish some new properties of Mersenne numbers. [ABSTRACT FROM AUTHOR]

Abstract: We deal here with the geometry of the so-called twistor fibration over the De Sitter 3-space, where the total space is a five-dimensional reductive homogeneous space with two canonical invariant almost CR structures. Fixed the normal metric on we study the harmonic map equation for smooth maps of Riemann surfaces into . A characterization of spacelike surfaces with harmonic twistor lifts to is obtained. Also it is shown that the harmonic map equation for twistor lifts can be formulated as the curvature vanishing of an -loop of connections i.e. harmonic twistor lifts exist within -families. Special harmonic maps such as holomorphic twistor lifts are also considered and some remarks concerning (compact) vacua of the twistor energy are given. [ABSTRACT FROM AUTHOR]

The article features geometer German Fedorovich Laptev in commemoration of his 100th birthday on June 30, 2009. It says that Laptev attended the Kazan' University in 1926, which held international competitions for outstanding mathematicians in honor of Nikolai Ivanovich Lobachevskii. It states that Laptev became a follower of a Lobachevskii competition winner Elie Cartan in introducing the movable-frame method. It mentions that Laptev's main scientific work has been called the Laptev method.

This special section is the outcome of the graph transformation tool contest organised during the Graph-Based Tools (GraBaTs) 2008 workshop, which took place as a satellite event of the International Conference on Graph Transformation (ICGT) 2008. The contest involved two parts: three “off-line case studies” which were published before the contest, and to which solutions were submitted and reviewed; and a “live contest” for which the case description was only handed out during the event, and to which solutions had to be constructed during a single afternoon session. Here we briefly sketch the off-line cases, and the setup and topic of the live contest in somewhat more detail. We also evaluate the results of the workshop, and give some recommendations for future editions. Finally, we introduce the research papers appearing in this special section. [ABSTRACT FROM AUTHOR]

Reverse and roundtrip engineering have become important research topics in model driven engineering. In this paper, we report on the use of model-to-model transformer (MoTMoT), a tool for model transformation (Schippers et al. in Satellite of the second international conference on graph transformation, vol 127, issue 3, pp 5–16, 2004), for the realization of a number of refactoring operations; this was proposed as a case study at GraBaTs 2008. MoTMoT is based on the story driven modeling (SDM) language for graph rewriting; thus the refactorings modify a graph model derived from Java source code. Realizing the three refactorings proposed in the case study allows us to demonstrate the strengths and weaknesses of the tool, but it also forces us to consider numerous issues that require the use of standard compliant mechanisms. The case study highlights the benefits of MoTMoT as a transformation engine. Among the advantages of MoTMoT, we may mention that MoTMoT does not depend on a particular modeling tool to represent transformations, and the input models may be produced by arbitrary UML tools, separately from MoTMoT. This is in contrast to other transformation tools which depend on a custom built modeling tool. Moreover, MoTMoT can easily be extended with new language features to improve its support for model transformation. The underlying transformation language, SDM, is based on a very powerful paradigm and is capable of expressing the preconditions and checks required by the case study. We also address other, more general challenges of this case study: conciseness, readability, maintainability, efficiency and scalability are important features for the implementation. MoTMoT turns out to be a robust tool that provides an answer to these challenges. [ABSTRACT FROM AUTHOR]

In this paper a relation between Bessel and Fourier Cosine transforms is obtained with the aid of Riemann-Liouville fractional integral. An application of this relation to weighted norm inequalities is given. [ABSTRACT FROM AUTHOR]

In this paper, we establish several very basic formulas relating convolution products, integral transforms and inverse integral transforms for functionals in L2(C0[0, T]). The expansion of functionals in L2(C0[0, T]) in terms of Fourier-Hermite functionals plays a key role. [ABSTRACT FROM AUTHOR]

In this paper, several properties associated with the complete monotonicity, the strongly complete monotonicity and the logarithmically complete monotonicity of functions related to the gamma and psi functions are obtained. Relevant connections of the results presented here with those derived in earlier works are also pointed out. [ABSTRACT FROM AUTHOR]

We define a new functional which is gauge invariant on the space of all smooth connections of a vector bundle over a compact Riemannian manifold. This functional is a generalization of the classical Yang-Mills functional. We derive its first variation formula and prove the existence of critical points. We also obtain the second variation formula. [ABSTRACT FROM AUTHOR]

By applying the Sears non-terminating transformations, we establish four general transformation theorems for double basic hypergeometric series of type Φ2:0;μ2:1;λ. Moreover, several transformation, reduction and summation formulae on the double basic hypergeometric series Φ2:0;12:1;2, Φ2:0;22:1;3 and Φ2:0;32:1;4 are also derived through parameter specialisation. [ABSTRACT FROM AUTHOR]

A new angular measure in Minkowski plane was introduced recently. It is additive, invariant under invertible linear transformations, and has a clear interpretation as an "amount of rotation" from one direction to another one. The total angle τ around a point depends on the unit ball. It is known that $$4.443 \approx \sqrt{2}\pi \leq \tau \leq 8$$. We show that $$4.985 \approx 4 \sqrt{2}\, {\rm ln}\,{\rm tan} \frac{3\pi}{8} \leq \tau \leq 8\, {\rm ln}\,{\rm tan} \frac{3\pi}{8}\, \approx 7.051$$. [ABSTRACT FROM AUTHOR]

Abstract: There is accumulating evidence that oxidative stress plays an important role in aging. Our previous phosphoproteomic study of the human neuroblastoma cell line SH-SY5Y revealed changes in the phosphorylation of several proteins such as lamin A/C during 6-hydroxydopamine-induced oxidative stress. The present study employed native proteomic analysis to clarify protein–protein interaction under physiological conditions. We examined oxidative stress-related changes in SH-SY5Y cellular proteins using blue-native polyacrylamide gel electrophoresis (BN-PAGE), a powerful tool for the separation of protein complexes. BN-PAGE gel images showed successful separation of several complexes. Components of these complexes, separated by 2-D BN-PAGE in combination with SDS–PAGE, were identified by peptide mass fingerprinting employing MALDI-TOF MS and an MS/MS ion search on LC-MS/MS. TCP-1 complex, ATP synthase, and the complex of heat shock protein 90 with its client proteins such as pyruvate kinase were detected. Two dimensional BN-PAGE and Western blot analysis revealed an increase of lamin A/C associated with heat shock protein 90 in response to 6-OHDA-induced oxidative stress. [Copyright &y& Elsevier]

Abstract  Guest-host interactions of haloperidol (Halo) with β-cyclodextrin (β-CD) have been investigated using several techniques including phase solubility diagrams (PSD), proton nuclear magnetic resonance (1H-NMR), X-ray powder diffractometry (XRPD), differential scanning calorimetry (DSC), scanning electron microscopy (SEM) and molecular mechanical modeling (MM+). From an analysis of the PSDs, both protonated and neutral Halo (pK a=8.5) form soluble 1:1 and 1:2 Halo/β-CD complexes, while the insoluble complex has 1:2 (Halo:β-CD) stoichiometry (BS-type PSD). Ionization of Halo reduces its tendency to complex with β-CD, where the protonated species at pH=4.6 and 6.0 have K 11 values of 100 L⋅mol−1 and 298 L⋅mol−1, respectively, compared with 2000 L⋅mol−1 for neutral species at pH=10.6. The hydrophobic character of Halo was found to provide 32% of the driving force for complex stability, whereas other factors including specific interactions contribute −15 kJ⋅mol−1. 1H-NMR and MM+ studies indicate the formation of isomeric 1:1 and 1:2 complexes, where the chlorophenyl, flurophenyl, piperidine and butanone moieties become included into separate β-CD cavities. The dominant driving force for complexation is evidently van der Waals with very little electrostatic contribution. PSD, 1H-NMR, XRPD, DSC and SEM studies indicate the formation of inclusion complexes in solution and in the solid state. [ABSTRACT FROM AUTHOR]

Abstract  1,6-Bis(2-formylphenyl) hexane (I) was derived from 1,6-dibromohexane with salicylaldehyde and K2CO3 and the ligand (L) was derived from compound I and 2,6-diaminopyridine. Then, the Cu(II), Ni(II), Pb(II), Zn(II), Cd(II), and La(III) complexes with L were synthesized by the reaction of this ligand and Cu(NO3)2 · 3H2O, Ni(NO3)2 · 6H2O, Pb(NO3)2, Zn(NO3)2 · 6H2O, Cd(NO3)2 · 6H2O, and La(NO3)3 · 6H2O, respectively. The ligand and its metal complexes were characterized by elemental analysis, IR, 1H and 13C NMR, UV-Vis spectra, magnetic susceptibility, conductivity measurements, and mass spectra. All complexes are diamagnetic and the Cu(II) complex is binuclear. [ABSTRACT FROM AUTHOR]

Abstract: The Camassa–Holm equation can be viewed as the geodesic equation on some diffeomorphism group with respect to the invariant metric. We derive the geodesic equations on that group with respect to the invariant metric, which we call the modified Camassa–Holm equation, and then study the well-posedness and dynamics of a modified Camassa–Holm equation on the unit circle S, which has some significant difference from that of Camassa–Holm equation, e.g., it does not admit finite time blowup solutions. [Copyright &y& Elsevier]

Abstract  The reactions of strontium and barium salicylates with iron nitrate gave heterometallic complexes {[FeSr2(Sal)2(SalH)2(NO3)(DMA)4]} n (I) and {[FeBa2(Sal)2(SalH)3(DMA)4(H2O)]} n (II). The solid compounds are one-dimensional coordination polymers where bridging function is performed by salicylic acid residues and the NO3− group (in I). The salicylic acid residues are coordinated in the chelating bridging mode, their denticity ranging from 2 to 5. The IR spectra, magnetic properties, and thermal behavior of the complexes were studied. [ABSTRACT FROM AUTHOR]

Abstract: In this work, the performance of advanced oxidation solar assisted photochemical treatments of synthetic phenolic type wastewaters was studied at natural pH conditions, and with phenol concentrations in the range of 180–733mg/L. The photochemical treatment was mediated with ferrioxalate and peroxide in two CPC (compound parabolic collector) photoreactors of different volumes and operation conditions (batch and with closed flow). Phenol transformation efficiencies of 100% and total COD reduction percentages of 85% were reached within the first hour of phototreatment, having as final product an aromatics free effluent, in both types of reactors. The ferrioxalate type complexes using mass ratios of oxalate/phenol=1.5, oxalate/Fe3+ =15 and H2O2/phenol>5.0 showed to be very effective in the treatment of these effluents, even at pH conditions close to neutrality, pH region in which the Fenton type processes begin to lose efficiency due to the precipitation of iron as a hydroxide. [Copyright &y& Elsevier]

A non-commutative version of the semi-discrete Toda equation is considered. A Lax pair and its Darboux transformations and binary Darboux transformations are found and they are used to construct two families of quasi-determinant solutions. [ABSTRACT FROM AUTHOR]

We characterize in terms of Darboux transformations the spaces in the Segal-Wilson rational Grassmannian, which lead to commutative rings of differential operators having coefficients which are rational functions of ex. The resulting subgrassmannian is parametrized in terms of trigonometric Calogero-Moser matrices. [ABSTRACT FROM AUTHOR]

We present Bäcklund transformations for the non-commutative anti-self-dual Yang-Mills equations where the gauge group is G = GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this approach are represented in terms of quasi-determinants and belong to a non-commutative version of the Atiyah-Ward ansatz. In the commutative limit, our results coincide with those by Corrigan, Fairlie, Yates and Goddard. [ABSTRACT FROM AUTHOR]

We show that every locally compact Polish group is isomorphic to the isometry group of a proper separable metric space. This answers a question of Gao and Kechris. We also analyze the natural action of the isometry group of a separable ultrametric space on the space. This leads us to a structure theorem representing an arbitrary separable ultrametric space as a bundle with an ultrametric base and with ultrahomogeneous fibers which are invariant under the action of the isometry group. [ABSTRACT FROM AUTHOR]

Abstract  The alkaline-earth metal complexes [M(Pta)2(15C5)] (M = Ca, Sr, and Ba; Pta is the 1,1,1-trifluoro-5,5-dimethylhexane-2,4-dionate anion; 15C5 is 15-crown-5) were obtained from PtaH and 15C5 in toluene. The complexes were characterized by IR and 1H NMR spectra and TGA data. The structures of [Ca(Pta)2(15C5)] and [Ba(Pta)2(15C5)] were confirmed by X-ray diffraction analysis. The volatility and thermal stability decrease in the order [Ca(Pta)2(15C5)] > [Sr(Pta)2(15C5)] > [Ba(Pta)2(15C5)]. [ABSTRACT FROM AUTHOR]

Abstract: The synthesis of a family of Os(VIII) alkylidene complexes, the highest oxidation state alkylidenes known to date, and their reactivity toward small organic molecules are reported. [Copyright &y& Elsevier]

The reactivity of complex [Ru(η6-p-cymene)(κ3P,N,O-Ph2PCH2P{NP(O)(OEt)2}Ph2)][SbF6]21 towards a variety of mono- and bidentate neutral ligands has been studied, allowing the high-yield synthesis of the novel half-sandwich Ru(ii) derivatives [Ru(η6-p-cymene)(L)(κ2P,O-Ph2PCH2P{NP(O)(OEt)2}Ph2)][SbF6]2 (L = NCMe 3a, NCEt 3b, PMe34a, PMe2Ph 4b, PMePh24c, PPh34d, P(OMe)35a, P(OEt)35b, P(OPh)35c, py 6, κ1P-dppm 7a, κ1P-dppe 7b), as well as the octahedral species [Ru(N⁁N)2(κ2P,O-Ph2PCH2P{NP(O)(OEt)2}Ph2)][SbF6]2 (N⁁N = bipy 8a, phen 8b). Deprotonation of complexes 8a,b, upon treatment with an excess of NaOH in CH2Cl2, generates the monocationic derivatives [Ru(N⁁N)2(κ2P,N-Ph2PC(H)P{NP(O)(OEt)2}Ph2)][Cl] (N⁁N = bipy 9a, phen 9b) in which the methanide anion adopts an unprecedented κ2P,N bidentate coordination mode. The structures of compounds 6, 8a and 9a have been determined by single-crystal X-ray diffraction methods. [ABSTRACT FROM AUTHOR]

Abstract: By using the bifunctional ligand, 8-hydroxyquinoline-functionalized organosilane (Q-Si), the new mesoporous material Q–MCM-41 covalently bonded with 8-hydroxyquinoline was synthesized. Through the ligand exchange reaction, the new near-infrared (NIR) luminescent mesoporous LnQ3–MCM-41 (Ln=Er, Nd, Yb) materials were prepared by linking the lanthanide quinolinate complexes to the ordered mesoporous Q–MCM-41 material. The LnQ3–MCM-41 materials were characterized by powder X-ray diffraction and N2 adsorption/desorption, and they all show the characteristic mesoporous structure of MCM-41 with highly uniform pore size distributions. Fluorescence spectra of these LnQ3–MCM-41 materials were recorded and the corresponding luminescence decay analyses were measured. After ligand-mediated excitation, all the emission spectra of the LnQ3–MCM-41 materials show the characteristic NIR-luminescence of the corresponding lanthanide ions via the intramolecular energy transfer from the ligands to the lanthanide ions. The good luminescent performances enable these NIR-luminescent mesoporous materials to have potential applications in optical amplification (operating at 1.3 or 1.5μm) and laser systems, etc. [Copyright &y& Elsevier]

Three new quinoxaline-based ligands with N,S-bidentate chelating sites, 2,3-bis(n-propylthiomethyl)quinoxaline (L1), 2,3-bis(tert-butylthiomethyl)quinoxaline (L2) and 2,3-bis[(o-aminophenyl)thiomethyl]quinoxaline (L3) have been synthesized and their coordination behavior with Ag(I) was studied. Four Ag(I) complexes varying from 0D to 3D have been obtained by these structurally related ligands with AgX (X = ClO4−, NO3−). Single crystal X-ray diffraction analyses show that the structures of 1and 2are directed by the counter-anions used in such a system: the reaction of L1with AgClO4yielded a tetranuclear molecular cage {[AgL1](ClO4)}4(1), while using AgNO3instead led to the formation of a 2D layer framework with ππ stacking {[Ag2L1(NO3)2](H2O)0.5}n(2). When L2was used instead of L1to react with AgNO3, a non-centrosymmetric 3D network with (82.9)2(82.9.10) topology [Ag3L2(NO3)3]n(3) was obtained, and L3instead of L1to react with AgClO4, a 1D chain with AgAg interaction {[Ag2L3(DMF)](ClO4)2(H2O)}n(4) was formed. The structural differences between 2and 3, 1and 4, respectively, clearly show the important effect of the terminal groups of ligands on the structural modulation in such coordination architectures. Moreover, there are two coordination modes of S atoms in 1–4: one is µ2-bridging (in 2and 3), and the other is a mono-coordination (in 1and 4). In addition, the luminescence properties of these compounds have also been studied in solid state at room temperature. [ABSTRACT FROM AUTHOR]

Abstract: The topological Tverberg theorem claims that for any continuous map of the -simplex to there are q disjoint faces of such that their images have a non-empty intersection. This has been proved for affine maps, and if q is a prime power, but not in general. We extend the topological Tverberg theorem in the following way: Pairs of vertices are forced to end up in different faces. This leads to the concept of constraint graphs. In Tverberg''s theorem with constraints, we come up with a list of constraints graphs for the topological Tverberg theorem. The proof is based on connectivity results of chessboard-type complexes. Moreover, Tverberg''s theorem with constraints implies new lower bounds for the number of Tverberg partitions. As a consequence, we prove Sierksma''s conjecture for and . [Copyright &y& Elsevier]

Abstract: Schiff bases of 1′-hydroxy-2′-acetonaphthone (HAN) containing chalcogen functionalities, 1-HO–C10H6-2-CH3)C(CH2) n EC6H4-4-R (R=H or OMe; n =2 or 3; E=S (L 1–L 2), Se (L 3–L 4) or Te (L 5–L 6)) have been synthesized in yield 90–95%. They show characteristic 1H, 13C{1H} 77Se{1H} and 125Te{1H} (in case of selenated and tellurated species, respectively) NMR spectra. Their complexation with Pd(II), Pt(II), Hg(II) and (p-cymene)Ru(II) has been explored. The single-crystal structures of ligands L 1, L 3 and L 6 and complexes of Pd(II) with L 1, L 2, L 3 and L 5 have been determined. The geometry of Pd is close to square planar in all the complexes and the ligands coordinate in a uni-negative tridentate mode. The Pd–N bond lengths are in the range 1.996(7)–2.019(5)Ǻ. The Pd–Se bond distance is 2.3600(5)Ǻ whereas Pd–Te is 2.5025(7)Ǻ. The Pd(II) complexes of L 1–L 5 have been found promising as homogeneous catalyst for Heck and Suzuki reactions. The yields obtained were up to 85%. [Copyright &y& Elsevier]