In a laboratory olfactometer, 12% of female Aedes aegypti with a marker gene for red eye (re), 0.7% of females with a marker gene for white eye (we), and 54.1% of females with normal (norm) eye color were attracted to odor from a human hand. When a synthetic attractant blend was used in place of the hand, the attraction rate was 7%, 0.3%, and 35.4%, respectively. On average, re females required...

Mosquito repellent lotions generally use ingredients such as diethyltoluamide (DEET). DEET has been mixed by the manufacture of commercial mosquito and used consumers without regard to consequences if it is continuing used. Though many natural plants, especially marine plants can also provide same benefits a repellent. Therefore, in this study aim was make lotion based on seaweed (Sargassum pol...

For a particular class of integral operators K we show that the quantity φ := log det (I +K)− log det (I −K) satisfies both the integrated mKdV hierarchy and the sinh-Gordon hierarchy. This proves a conjecture of Zamolodchikov.

Such a rotation g can be described by three parameters. For instance, if you know the axis of rotation (specified by a direction or a point on S or two angles) and the angle of rotation (one parameter), g is determined uniquely. Alternatively, a matrix g ∈ R3×3 has 9 entries, but the requirement that gg = 1 gives 6 conditions on these entries, and again 9− 6 = 3. (The condition that det g = 1 s...

For a particular class of integral operators K we show that the quantity φ := log det (I + K)log det (/ K) satisfies both the integrated mKdV hierarchy and the Sinh-Gordon hierarchy. This proves a conjecture of Zamolodchikov.

We compute the functional determinant quotient (det P h)=(det P g) for the Paneitz operator P in conformally related Riemannian metrics g; h, and discuss related positivity questions.

The Teichmüller space Teich(S) of a surface S in genus g > 1 is a totally real submanifold of the quasifuchsian space QF(S). We show that the determinant of the Laplacian det′(∆) on Teich(S) has a unique holomorphic extension to QF(S). To realize this holomorphic extension as the determinant of differential operators on S, we introduce a holomorphic family {∆μ,ν} of elliptic second order differ...

Carlitz, Handa, and Mohanty proved determinantal formulas for counting partitions contained in a fixed bounding shape by area. Gessel and Viennot introduced a combinatorial method for proving such formulas by interpreting the determinants as counting suitable configurations of signed lattice paths. This note describes an alternative combinatorial approach that uses sign-reversing involutions to...

The classical action of a two dimensional N = 2 supersymmetric theory, characterized by a general Kähler potential, is written down on a non(anti)commutative superspace. The action has a power series expansion in terms of the determinant of the non(anti)commutativity parameter C αβ. The theory is explicitly shown to preserve half of the N = 2 supersymmetry, to all orders in (det C) n. The resul...

Lemma 8.4 If C is a n n × matrix with 0 det ≠ C , then, there exists a n n × (complex) matrix B such that C e = . Proof: For any matrix C , there exists an invertible matrix P , s.t. 1 P CP J − = , where J is a Jordan matrix. If C e = , then, 1 1 1 P B P B e P e P P CP J − − − = = = . Therefore, it is suffice to prove the result when C is in a canonical form. Suppose that 1 ( , , ) s C diag C C...