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- Combinatorics (2)
- Dirichlet problem (2)
- Fibonacci numbers (2)
- Borsuk-Ulam theorem (1)
- Cancer; Tumor; Vaccine; Immunotherapy; Population models; Competition models; Mathematical modeling; Immune system; Ordinary differential equations (1)
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- Cantor-Bendixson derivatives (1)
- Combinatorial identities (1)
- Deformation lemma (1)
- Fair division (1)
- Fibonacci sums (1)
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- Nodec space (1)
- Nonlinear elliptic equations (1)
- Quasi P-space (1)
- Quasinormality (1)
- Scattered space (1)
- Sign-changing (1)
- Sign-changing solution (1)
- Subcritical (1)
- Superlinear (1)
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Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
A Combinatorial Approach To Hyperharmonic Numbers, Arthur T. Benjamin, David Gaebler '04, Robert Gaebler '04
A Combinatorial Approach To Hyperharmonic Numbers, Arthur T. Benjamin, David Gaebler '04, Robert Gaebler '04
All HMC Faculty Publications and Research
Hyperharmonic numbers arise by taking repeated partial sums of harmonic numbers. These numbers can be expressed in terms of r-Stirling numbers, leading to combinatorial interpretations of many interesting identities.
A Probabilistic View Of Certain Weighted Fibonacci Sums, Arthur T. Benjamin, Judson D. Neer, Daniel T. Otero, James A. Sellers
A Probabilistic View Of Certain Weighted Fibonacci Sums, Arthur T. Benjamin, Judson D. Neer, Daniel T. Otero, James A. Sellers
All HMC Faculty Publications and Research
In this article, we pursue the reverse strategy of using probability to derive an and develop an exponential generating function for an in Section 3. In Section 4, we present a method for finding an exact, non-recursive, formula for an.
The Fibonacci Numbers -- Exposed More Discretely, Arthur T. Benjamin, Jennifer J. Quinn
The Fibonacci Numbers -- Exposed More Discretely, Arthur T. Benjamin, Jennifer J. Quinn
All HMC Faculty Publications and Research
No abstract provided in this article.
A Sign-Changing Solution For A Superlinear Dirichlet Problem, Ii, Alfonso Castro, Pavel Drabek, John M. Neuberger
A Sign-Changing Solution For A Superlinear Dirichlet Problem, Ii, Alfonso Castro, Pavel Drabek, John M. Neuberger
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In previous work by Castro, Cossio, and Neuberger [2], it was shown that a superlinear Dirichlet problem has at least three nontrivial solutions when the derivative of the nonlinearity at zero is less than the first eigenvalue of -Δ with zero Dirichlet boundry condition. One of these solutions changes sign exactly-once and the other two are of one sign. In this paper we show that when this derivative is between the k-th and k+1-st eigenvalues there still exists a solution which changes sign at most k times. In particular, when k=1 the sign-changing exactly-once solution persists although one-sign solutions no …
Consensus-Halving Via Theorems Of Borsuk-Ulam And Tucker, Forrest W. Simmons, Francis E. Su
Consensus-Halving Via Theorems Of Borsuk-Ulam And Tucker, Forrest W. Simmons, Francis E. Su
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In this paper we show how theorems of Borsuk-Ulam and Tucker can be used to construct a consensus-halving: a division of an object into two portions so that each of n people believes the portions are equal. Moreover, the division takes at most n cuts, which is best possible. This extends prior work using methods from combinatorial topology to solve fair division problems. Several applications of consensus-halving are discussed.
A Mathematical Model Of Immune Response To Tumor Invasion, Lisette De Pillis, Ami Radunskaya
A Mathematical Model Of Immune Response To Tumor Invasion, Lisette De Pillis, Ami Radunskaya
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Recent experimental studies by Diefenbach et al. [1] have brought to light new information about how the immune system of the mouse responds to the presence of a tumor. In the Diefenbach studies, tumor cells are modified to express higher levels of immune stimulating NKG2D ligands. Experimental results show that sufficiently high levels of ligand expression create a significant barrier to tumor establishment in the mouse. Additionally, ligand transduced tumor cells stimulate protective immunity to tumor rechallenge. Based on the results of the Diefenbach experiments, we have developed a mathematical model of tumor growth to address some of the questions …
The Effect Of The Domain Topology On The Number Of Minimal Nodal Solutions Of An Elliptic Equation At Critical Growth In A Symmetric Domain, Alfonso Castro, Mónica Clapp
The Effect Of The Domain Topology On The Number Of Minimal Nodal Solutions Of An Elliptic Equation At Critical Growth In A Symmetric Domain, Alfonso Castro, Mónica Clapp
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We consider the Dirichlet problem Δu + λu + |u|2*−2u = 0 in Ω, u = 0 on ∂Ω where Ω is a bounded smooth domain in RN, N≥4, and 2* = 2N/(N−2) is the critical Sobolev exponent. We show that if Ω is invariant under an orthogonal involution then, for λ>0 sufficiently small, there is an effect of the equivariant topology of Ω on the number of solutions which change sign exactly once.
Spaces X In Which All Prime Z-Ideals Of C(X) Are Minimal Or Maximal, Melvin Henriksen, Jorge Martinez, R. G. Woods
Spaces X In Which All Prime Z-Ideals Of C(X) Are Minimal Or Maximal, Melvin Henriksen, Jorge Martinez, R. G. Woods
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Quasi P-spaces are defined to be those Tychonoff spaces X such that each prime z-ideal of C(X) is either minimal or maximal. This article is devoted to a systematic study of these spaces, which are an obvious generalization of P-spaces. The compact quasi P-spaces are characterized as the compact spaces which are scattered and of Cantor-Bendixson index no greater than 2. A thorough account of locally compact quasi P-spaces is given. If X is a cozero-complemented space and every nowhere dense zeroset is a z-embedded P-space, then X is a quasi P-space. Conversely, if X is a quasi P-space and …