A Study of Electrospray Ionization Emitters with Differing Geometries with Respect to Flow Rate and Electrospray Voltage

The performance of several electrospray ionization emitters with different orifice inside diameters (i.d.s), geometries, and materials are compared. The sample solution is delivered by pressure driven flow, and the electrospray ionization voltage and flow rate are varied systematically for each emitter investigated, while the signal intensity of a standard is measured. The emitters investigated include a series of emitters with a tapered outside diameters (o.d.) and unaltered i.d.s, a series of emitters with tapered o.d.s and i.d.s, an emitter with a monolithic frit and a tapered o.d., and an emitter fabricated from polypropylene. The results show that for the externally etched emitters, signal was nearly independent of i.d. and better ion utilization was achieved at lower flow rates. Furthermore, emitters with a 50 μm i.d. and an etched o.d. produced about 1.5 times more signal than etched emitters with smaller i.d.s and about 3.5 times more signal than emitters with tapered inner and outer dimensions. Additionally, the work presented here has important implications for applications in which maximizing signal intensity and reducing frictional resistance to flow are necessary. Overall, the work provides an initial assessment of the critical parameters that contribute to maximizing the signal for electrospray ionization sources interfaced with pressure driven flows.     

An integro-differential equation for surface ocean waves with finite depth

An explicit integro-differential equation formulation is derived for surface ocean waves with finite depth. The equation involves only 2D surface variables. For this equation, we establish the stability and existence of solutions, and explain the effect of depth on surface wave properties.     

Cleaning Random d-Regular Graphs with Brooms

A model for cleaning a graph with brushes was recently introduced. Let α = (v ₁, v ₂, . . . , v _n ) be a permutation of the vertices of G; for each vertex v _i let ${N^+(v_i)=\{j: v_j v_i \in E {\rm and} j>\,i\}}${N^+(v_i)=\{j: v_j v_i \in E {\rm and} j>\,i\}} and N^-(v_i)={j: v_j v_i ? E and j <  i}{N^-(v_i)=\{j: v_j v_i \in E {\rm and} j<\,i\}} ; finally let b_a(G)=?_i=1ⁿ max{|N⁺(v_i)|-|N^-(v_i)|,0}{b_{\alpha}(G)=\sum_{i=1}^n {\rm max}\{|N^+(v_i)|-|N^-(v_i)|,0\}}. The Broom number is given by B(G) =  max _α b _α (G). We consider the Broom number of d-regular graphs, focusing on the asymptotic number for random d-regular graphs. Various lower and upper bounds are proposed. To get an asymptotically almost sure lower bound we use a degree-greedy algorithm to clean a random d-regular graph on n vertices (with dn even) and analyze it using the differential equations method (for fixed d). We further show that for any d-regular graph on n vertices there is a cleaning sequence such at least n(d + 1)/4 brushes are needed to clean a graph using this sequence. For an asymptotically almost sure upper bound, the pairing model is used to show that at most n(d+2?{d ln2})/4{n(d+2\sqrt{d \ln 2})/4} brushes can be used when a random d-regular graph is cleaned. This implies that for fixed large d, the Broom number of a random d-regular graph on n vertices is asymptotically almost surely \fracn4(d+Q(?d)){\frac{n}{4}(d+\Theta(\sqrt{d}))}.     

A systematic study of neutral and charged 3d-metal trioxides and tetraoxides

Using density functional theory with generalized gradient approximation, we have performed a systematic study of the structure and properties of neutral and charged trioxides (MO(3)) and tetraoxides (MO(4)) of the 3d-metal atoms. The results of our calculations revealed a number of interesting features when moving along the 3d-metal series. (1) Geometrical configurations of the lowest total energy states of neutral and charged trioxides and tetraoxides are composed of oxo and∕or peroxo groups, except for CuO(3)(-) and ZnO(3)(-) which possess a superoxo group, CuO(4)(+) and ZnO(4)(+) which possess two superoxo groups, and CuO(3)(+), ZnO(3)(+), and ZnO(4)(-) which possess an ozonide group. While peroxo groups are found in the early and late transition metals, all oxygen atoms bind chemically to the metal atom in the middle of the series. (2) Attachment or detachment of an electron to∕from an oxide often leads to a change in the geometry. In some cases, two dissociatively attached oxygen atoms combine and form a peroxo group or a peroxo group transforms into a superoxo group and vice versa. (3) The adiabatic electron affinity of as many as two trioxides (VO(3) and CoO(3)) and four tetraoxides (TiO(4), CrO(4), MnO(4), and FeO(4)) are larger than the electron affinity of halogen atoms. All these oxides are hence superhalogens although only VO(3) and MnO(4) satisfy the general superhalogen formula.     

Group connectivity in line graphs

Tutte introduced the theory of nowhere zero flows and showed that a plane graph G has a face k-coloring if and only if G has a nowhere zero A-flow, for any Abelian group A with |A|≥k. In 1992, Jaeger et al. [9] extended nowhere zero flows to group connectivity of graphs: given an orientation D of a graph G, if for any b:V(G)?A with ∑_v∈V(G)b(v)=0, there always exists a map f:E(G)?A−{0}, such that at each v∈V(G), in A, then G is A-connected. Let Z₃ denote the cyclic group of order 3. In [9], Jaeger et al. (1992) conjectured that every 5-edge-connected graph is Z₃-connected. In this paper, we proved the following.

• (i) 

  Every 5-edge-connected graph is Z3-connected if and only if every 5-edge-connected line graph is Z3-connected.

• (ii) 

  Every 6-edge-connected triangular line graph is Z3-connected.

• (iii) 

  Every 7-edge-connected triangular claw-free graph is Z3-connected.

In particular, every 6-edge-connected triangular line graph and every 7-edge-connected triangular claw-free graph have a nowhere zero 3-flow.     

Orbit of an image under iterated system

An orbital picture depicts the path of an object under semi-group of transformations. The concept initially given by Barnsley [3] has utmost importance in image compression, biological modeling and other areas of fractal geometry. In this paper, we introduce superior iterations to study the role of linear and nonlinear transformations on the orbit of an object. Various characteristics of the computed figures have been discussed to indicate the usefulness of study in mathematical analysis. Modified algorithms are given to compute the orbital picture and V-variable orbital picture. An algorithm to calculate the distance between images makes the study motivating. A brief discussion about the proof of the Cauchy sequence of images is also given.     

Dyadic Bivariate Wavelet Multipliers in L^2（R@2）

The single 2 dilation wavelet multipliers in one-dimensional case and single A-dilation (where A is any expansive matrix with integer entries and |detA| = 2) wavelet multipliers in twodimensional case were completely characterized by Wutam Consortium (1998) and Li Z., et al. (2010). But there exist no results on multivariate wavelet multipliers corresponding to integer expansive dilation matrix with the absolute value of determinant not 2 in L ²(ℝ²). In this paper, we choose $2I_2 = \left( {{*{20}c} 2 & 0 \\ 0 & 2 \\ } \right)$2I_2 = \left( {\begin{array}{*{20}c} 2 & 0 \\ 0 & 2 \\ \end{array} } \right) as the dilation matrix and consider the 2I ₂-dilation multivariate wavelet Φ = {ψ ₁, ψ ₂, ψ ₃}(which is called a dyadic bivariate wavelet) multipliers. Here we call a measurable function family f = {f ₁, f ₂, f ₃} a dyadic bivariate wavelet multiplier if Y₁ = { F ^{- 1} ( f₁ [^(y₁ )] ),F ^{- 1} ( f₂ [^(y₂ )] ),F ^{- 1} ( f₃ [^(y₃ )] ) }\Psi _1 = \left\{ {\mathcal{F}^{ - 1} \left( {f_1 \widehat{\psi _1 }} \right),\mathcal{F}^{ - 1} \left( {f_2 \widehat{\psi _2 }} \right),\mathcal{F}^{ - 1} \left( {f_3 \widehat{\psi _3 }} \right)} \right\} is a dyadic bivariate wavelet for any dyadic bivariate wavelet Φ = {ψ ₁, ψ ₂, ψ ₃}, where [^(f)]\hat f and F ⁻¹ denote the Fourier transform and the inverse transform of function f respectively. We study dyadic bivariate wavelet multipliers, and give some conditions for dyadic bivariate wavelet multipliers. We also give concrete forms of linear phases of dyadic MRA bivariate wavelets.     

Six-flows on almost balanced signed graphs

In 1983, Bouchet conjectured that every flow-admissible signed graph admits a nowhere-zero 6-flow. By Seymour's 6-flow theorem, Bouchet's conjecture holds for signed graphs with all edges positive. Recently, Rollová et al proved that every flow-admissible signed cubic graph with two negative edges admits a nowhere-zero 7-flow, and admits a nowhere-zero 6-flow if its underlying graph either contains a bridge, or is 3-edge-colorable, or is critical. In this paper, we improve and extend these results, and confirm Bouchet's conjecture for signed graphs with frustration number at most two, where the frustration number of a signed graph is the smallest number of vertices whose deletion leaves a balanced signed graph.     

A pyridine-containing ruthenium–indenylidene complex: Synthesis and activity in ring-closing metathesis

The reaction of Cl₂Ru(PCy₃)₂(3-phenylindenylidene) with excess pyridine leads to the new pyridine-containing ruthenium-based complex: Cl₂Ru(PCy₃)(Py)₂(3-phenylindenylidene) in good yield. This catalyst has been fully characterized and tested in ring-closing metathesis. Its moderate activity has been examined by kinetic studies using several substrates and different reaction conditions.