Let h and g be two positive integers. We fix an element Ω of the Siegel upper half plane H g := Z ∈ C (g,g) | Z = t Z, Im Z > 0 of degree g once and for all. Let M be positive symmetric, even integral matrix of degree h. An entire function f on C (h,g) satisfying the transformation behaviour F (W + ξΩ + η) = exp −πiσ(M(ξΩ t ξ + 2W t ξ)) f (W) for all W ∈ C (h,g) and (ξ, η) ∈ Z (h,g) × Z (h,g) i...

This paper establishes Hölder estimates of Du and Lp estimates of D2u for solutions u to the parabolic Monge-Ampère equation −Aut + ( det D2u)1/n = f .

Two U.S. military issue deet repellent formulations (75% deet liquid and 33% deet lotion) and Avon Skin-So-Soft were tested against ceratopogonid midges under field conditions in Honduras. Test subjects were U.S. military personnel deployed to Honduras for training. Culicoides furens accounted for 96.3% of all midges collected. The liquid and lotion formulations of deet and Avon Skin-So-Soft pr...

The use of insect repellent has increased during recent years to prevent insect stings and its feared consequences of virus and parasitic diseases transmitted by infected mosquitoes and tick bites. DEET (N, N-diethyl-3-toluamide) is the most effective and most widely-used insect repellent and it is used by approximately 30% of the population. The DEET Registry is a post-marketing surveillance s...

• ρ ramifies at only finitely many places. • ρ is odd, i.e., det ρ(c) = −1 for all complex conjugations c ∈ GF . • ρ is potentially crystalline and ordinary at all places above p. • ρ|GF (ζp) is absolutely irreducible. • There exists a parallel weight two Hilbert modular form f such that ρf is potentially crystalline and ordinary at all places above p and ρ = ρf . Then there exists a Hilbert mo...

Previous work has investigated adults' knowledge of principles for arithmetic with positive numbers (Dixon, Deets, & Bangert, 2001). The current study extends this past work to address adults' knowledge of principles of arithmetic with a negative number, and also investigates links between knowledge of principles and problem representation. Participants (N = 44) completed two tasks. In the Eval...

Pure DEET is a water-white to amber-color liquid. It is mainly used as a commercial insect or acarid repellent. In 1990, approximately 4 million pounds of the active ingredient DEET was used in commercial products and the average annual domestic use of DEET has been estimated as ranging from 5 to 7 million pounds based on product sales. Aquatic systems appear to be the main environmental sink f...

The affine synthesis operator Sc = P j>0 P k∈Z d c j,k ψ j,k is shown to map the coefficient space ℓ p (Z+ × Z d) surjectively onto L p (R d), for p ∈ (0, 1]. Here ψ j,k (x) = | det aj| 1/p ψ(ajx − k) for dilation matrices aj that expand , and the synthesizer ψ ∈ L p (R d) need satisfy only mild restrictions, for example ψ ∈ L 1 (R d) with nonzero integral or else with periodization that is rea...

In 1980, Itzykson and Zuber presented their result on a certain integral over the unitary group which had great impact in several areas of mathematical physics. Let U be a matrix parameterizing the unitary group U(N) with the invariant Haar measure dμ(U). Moreover, consider two diagonal matrices x and y with entries xn and yn, respectively, where n = 1, . . . , N . The Itzykson-Zuber integral c...

We present new, simple proofs for the enumeration of five of the ten symmetry classes of plane partitions contained in a given box. Four of them are derived from a simple determinant evaluation, using combinatorial arguments. The previous proofs of these four cases were quite complicated. For one more symmetry class we give an elementary proof in the case when two of the sides of the box are eq...