The simplified solution algorithm for an integrated supplier-buyer inventory model with two-part trade credit in a supply chain system

Ho et al. [Ho, C.H., Ouyang, L.Y., Su, C.H., 2008. Optimal pricing, shipment and payment policy for an integrated supplier-buyer inventory model with two-part trade credit, European Journal of Operational Research 187, 496-510] discussed the integrated inventory model with two-part trade credit and presented an algorithm to solve it. Basically, Ho et al.’s inventory model is correct and interesting. However, this paper indicates that the solution algorithm described in Ho et al. (2008) can be simplified further. So, this paper can not only derive the optimally closed-form formulations for the optimal numbers of shipments but also develop different algorithms to improve those in Ho et al. (2008). Numerical examples illustrate that the algorithm to locate the optimal solution is rather accurate and rapid.     

On Projective Planes of Order 15 Admitting a Collineation of Order 7

In this article we prove that there is no projective plane of order 15 admitting a collineation group of order 21. C. Y. Ho proved that there is no projective plane of order 15 admitting a collineation group of order 49. But his proof is incorrect. We also correct his error. The conclusion remains the same. We used a computer for our research.     

Note on the m-step competition numbers of paths and cycles

Since Cohen introduced the competition graph in 1968, the competition graph has been studied widely and many variations of it have been discussed. In 2000, Cho, Kim and Nam defined and studied the m-step competition graph and computed the 2-step competition numbers of paths and cycles. Recently, Ho gave bounds for the m-step competition numbers of paths and cycles. In this paper we continue to study the m-step competition numbers of paths and cycles, partially improve the results of Ho on the upper bounds of the m-step competition numbers of paths and cycles, and show that a conjecture posed by Ho is not true.     

BRILL－NOETHER MATRIX FOR RANK TWO VECTOR BUNDLES

Lei X be an arbitrary smooth irreducible complex projective curve, E (?) X a rank two vector bundle generated by its sections. The author first represents E as a triple {D1,D2,f}, where D1 , D2 are two effective divisors with d = deg(D1) + deg(D2), and f ∈ H0(X, [D1] |D2) is a collection of polynomials. E is the extension of [D2] by [D1] which is determined by f. By using f and the Brill-Noether matrix of D1 + D2, the author constructs a 2g X d matrix WE whose zero space gives Im{H0(X,[D1]) (?) H0(X, [D1] |D1)}(?)Im{H0(X, E) (?) H0(X,[D2]) (?) H0(X,[D2] |D2)}. From this and H0(X,E) = H0(X, [D1]) (?) Im{H0(X, E) (?) H0(X, [D2])}, it is got in particular that dimH0(X, E) = deg(E) - rank(WE) + 2.     

Anomaly cancellation and modularity,II: The <Emphasis Type="Italic">E</Emphasis><Subscript>8</Subscript> ×<Emphasis Type="Italic">E</Emphasis><Subscript>8</Subscript> case

In this paper we show that both of the Green-Schwarz anomaly factorization formula for the gauge group E ₈ × E ₈ and the Ho?ava-Witten anomaly factorization formula for the gauge group E8 can be derived through modular forms of weight 14. This answers a question of Schwarz. We also establish generalizations of these factorization formulas and obtain a new Ho?ava-Witten type factorization formula.     

New-from-old full dualities via axiomatisation

We study different full dualities based on the same finite algebra. Our main theorem gives conditions on two different alter egos of a finite algebra under which, if one yields a full duality, then the other does too. We use this theorem to obtain a better understanding of several important examples from the theory of natural dualities. We also clarify what it means for two full dualities based on the same finite algebra to be different. Throughout the paper, a fundamental role is played by the universal Horn theory of the dual categories.     

Sharp bounds for singular values of fractional integral operators

From the results of Dostanic [M.R. Dostanic, Asymptotic behavior of the singular values of fractional integral operators, J. Math. Anal. Appl. 175 (1993) 380-391] and V? and Gorenflo [Kim Tuan V?, R. Gorenflo, Singular values of fractional and Volterra integral operators, in: Inverse Problems and Applications to Geophysics, Industry, Medicine and Technology, Ho Chi Minh City, 1995, Ho Chi Minh City Math. Soc., Ho Chi Minh City, 1995, pp. 174-185] it is known that the jth singular value of the fractional integral operator of order α>0 is approximately (πj)^−α for all large j. In this note we refine this result by obtaining sharp bounds for the singular values and use these bounds to show that the jth singular value is (πj)^−α[1+O(j⁻¹)].     

K(a)hler Manifolds with Almost Non-negative Ricci Curvature

Compact K(a)hler manifolds with semi-positive Ricci curvature have been investigated by various authors. From Peternell's work, if M is a compact K(a)hler n-manifold with semi-positive Ricci curvature and finite fundamental group, then the universal cover has a decomposition (M) ≌ X1 × … × Xm, where Xj is a Calabi-Yau manifold, or a hyperK(a)hler manifold, or Xj satisfies Ho(Xj,Ωp) = 0. The purpose of this paper is to generalize this theorem to almost non-negative Ricci curvature K(a)hler manifolds by using the Gromov-Hausdorff convergence. Let M be a compact complex n-manifold with non-vanishing Euler number. If for any ε ＞ 0, there exists a K(a)hler structure (Je,ge) on M such that the volume Volge(M) ＜ V, the sectional curvature |K(gε)| ＜ Λ2, and the Ricci-tensor Ric(gε)＞ -εgε, where ∨ and Λ are two constants independent of ε. Then the fundamental group of M is finite, and M is diffeomorphic to a complex manifold X such that the universal covering of X has a decomposition, (X) ≌ X1 × … × Xs, where Xi is a Calabi-Yau manifold, or a hyperK(a)hler manifold, or Xi satisfies Ho(Xi, Ωp) = {0}, p ＞ 0.     

Some results,concerning the variation of eigenvalues,when these depend on a real parameter

In this article we deal with a Hamiltonial of the form H(v) = Ho + A(v) where Ho is a self-adjoint bounded or unbounded operator on a Hilbert space and A(v) is a bounded self-adjoint perturbation depending on a real parameter v. In quantum mechanics a variety of results has been obtained by taking formally the derivative of the eigenvectors and eigenvalues of H(v).The differentiability of the eigenvectors and eigenvalues has been rigorously proved under several assumptions. Among these assumptions is the assumption that the eigenvalues are simple and the assumption that the perturbation A(v) is a uniformly bounded self-adjoint operator. A part of this article is dealing with examples, which show that these two assumptions are essential. The rest of this article is devoted to different applications concerning asymptotic relations of eigenvalues and a result for the solutions of the equation d_y/d_t= M(t)y in an abstract infinite dimensional Hilbert space, where iM(t)(1²=-1) is self-adjoint for every t in an interval. This result finds a succesful application to the theory of Toda and Langmuir lattices.     

Moduli spaces of vector bundles over a Klein surface

A compact topological surface S, possibly non-orientable and with non-empty boundary, always admits a Klein surface structure (an atlas whose transition maps are dianalytic). Its complex cover is, by definition, a compact Riemann surface M endowed with an anti-holomorphic involution which determines topologically the original surface S. In this paper, we compare dianalytic vector bundles over S and holomorphic vector bundles over M, devoting special attention to the implications that this has for moduli varieties of semistable vector bundles over M. We construct, starting from S, totally real, totally geodesic, Lagrangian submanifolds of moduli varieties of semistable vector bundles of fixed rank and degree over M. This relates the present work to the constructions of Ho and Liu over non-orientable compact surfaces with empty boundary (Ho and Liu in Commun Anal Geom 16(3):617–679, 2008).     

A Correction to “Incidence Matrices and Collineations of Finite Projective Planes” by Chat Yin Ho, Designs, Codes and Cryptography, 18 (1999), 159–162

In this note we consider the set of incidence matrices of a cyclic projective planes whose set of points has cardinality a prime number p. We provide a correct proof of a result of Ho, showing that there exists an incidence matrix that possesses exactly p distinct eigenvalues.     

The Answer to a Problem Posed by Zhao and Ho

Zhao and Ho asked in a recent paper that for each T_0 space X, whether KB(X)(the set of all irreducible closed sets of X whose suprema exist) is the canonical k-bounded sobrification of X in the sense of Keimel and Lawson. In this paper, we construct a counterexample to give a negative answer. We also consider the subcategory Top_κ of the category Top_0 of T_0 spaces, and prove that the category KBSob of k-bounded sober spaces is a full reflective subcategory of the category Top_κ.     

Cyclic intersections and control of fusion

In this paper we study factorizable groups. An extension of a famous theorem of H. Wielandt on groups factorizable by two nilpotent subgroups of relatively prime orders is obtained. We also present a variant of a theorem of A. Gonçalves and C. Y. Ho.     

Valuation of sinking-fund bonds in the Vasicek and CIR frameworks∗Financial support from Murst Fondo 40% on ‘Modelli di struttura a termine dei tassi d'interesse’ is gratefully acknowledged.

In a sinking-fund bond, the issuer is required to retire portions of the bond prior to maturity, with the option of doing so either by calling the bonds by lottery, or by buying them back at their market value. This paper discusses the valuation of a default-free sinking-fund bond issue in the Vasicek (1977) and, alternatively, the Cox, Ingersoll and Ross (CIR) (1985) frameworks. We show in particular that, calling the bond issue without the delivery option ‘corresponding serial’, and the one without the prepayment feature ‘corresponding coupon’, under no-arbitrage a sinking-fund bond can be priced either in terms of the corresponding coupon bond and a bond call option, or in terms of the corresponding serial and a bond put option. We also present a detailed comparative-statics analysis of our valuation model, where we show that a sinking-fund bond has a stochastic duration intermediate between the ones of the corresponding serial and coupon bonds. We argue that such a feature gives a further rational for the presence of the delivery option. Moreover, we compare our results with the ones of Ho (1985), who has previously discussed the valuation problem under scrutiny.     

PSL(2,q) as a collineation group of projective planes of small order

Let Π be a projective plane of order n admitting a collineation group G≅PSL(2, q) for some prime power q. It is well known for n=q that Π must be Desarguesian. We show that if n<q then only finitely many cases may occur for П, all of which are Desarguesian. We obtain some information in case n=q ² with q odd, notably that G acts irreducibly on П for q≠3, 5, 9. The material herein was presented to the University of Toronto in partial fulfillment of the requirements for the degree of Doctor of Philosophy. The author is grateful to Professor Chat Y. Ho, presently at the University of Florida, for guidance in this research.     

A constructive proof of the Cartan-Dieudonné-Scherk Theorem in the real or complex case

The Cartan-Dieudonné-Scherk Theorem states that for fields of characteristic other than 2, every orthogonality can be written as the product of a certain minimal number of reflections across hyperplanes. The earliest proofs are not constructive, and constructive proofs either do not achieve minimal results or have been restricted to special cases. This paper presents a constructive proof in the real or complex field of the decomposition of a generalized orthogonal matrix into the product of the minimal number of generalized Householder matrices.     

Time heterogeneous programs of vaccination awareness: modeling and analysis

We investigate the role of time heterogeneity of public health systems efforts in favoring the propensity of parents to vaccinate their newborns against a target childhood disease. The starting point of our investigation is the behavioral-epidemiology model proposed by d’Onofrio et al. (PLoS ONE 7:e45653, 2012), where the PHS effort was assumed to be constant. We also consider the co-presence of another layer of temporal heterogeneity: seasonality in the contact rate of the disease. We mainly assume that the effort is periodic with a 1-year period because of alternating working and holiday periods. We show that if the average effort is larger than a threshold, then the disease can be eliminated leading to an ideal equilibrium point with \(100\%\) of vaccinated newborns. A more realistic disease-free equilibrium can also be reached, under a condition that depends on the whole form of the time profile describing the PHS effort. We also generalize our disease elimination-related results to a wide class of time-heterogenous PHS efforts. Finally, we analytically show that if the disease elimination is not reached, then the disease remains uniformly persistent.     

The Minimum Concave Cost Network Flow Problem with fixed numbers of sources and nonlinear arc costs

We prove that the Minimum Concave Cost Network Flow Problem with fixed numbers of sources and nonlinear arc costs can be solved by an algorithm requiring a number of elementary operations and a number of evaluations of the nonlinear cost functions which are both bounded by polynomials inr, n, m, wherer is the number of nodes,n is the number of arcs andm the number of sinks in the network.On leave from Institute of Mathematics, P.O. Box 631, Bo Ho, Hanoi, Vietnam.     

L~p CONTINUITY OF HRMANDER SYMBOL OPERATORS OpS_（0,0） ~m AND NUMERICAL ALGORITHM

If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ (0 ≤δ < ρ≤ 1). In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 (= F 0 , 2 1 ) → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p (= F 0 , 2 p ) → L p continuity for 1 < p < ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces.