Parsa Erfani and colleagues argue that a temporary intellectual property waiver for covid-19 vaccines is vital to increase supply, achieve global herd immunity, advance health equity

Consider three normal operators A,B,C on a separable Hilbert space ? as well scalar-valued spectral measures ? A ?(A), B ?(B) and C ?(C). For any ??L ? (? ×? ) X,Y?S 2 (?), the of Hilbert–Schmidt ?, we provide general definition triple operator integral ? (?)(X,Y) belonging to S (?) in such way that (?) belongs (S (?)×S (?),S (?)) bounded bilinear resulting mapping :L )?B is w * -continuous iso...

Denote by nA the sum of n copies of a Boolean algebra A. We prove that, for any countable Boolean algebra A, nA at mA with m > n implies nA a (n + \)A. In [2], W. Hanf constructed a Boolean algebra H isomorphic to the direct product H X H X H but not to H X H. This result of Hanf was strengthened by J. Ketonen in [4]: there exists even a countable Boolean algebra with this property. In [1], P. ...

Greek mathematician Diophantus of Alexandria noted that the numbers 1 16 , 33 16 , 68 16 and 105 16 have the property that the product of any two of them when increased by 1 is a square of a rational number. Let n be an integer. We say the set of natural numbers {a1, a2, . . . , am} has the property of Diophantus of order n, in brief D(n), if for all i, j = 1, 2, . . . ,m, i 6= j, the following...

Let F be a union-closed family of subsets of an m-element set A. Let n = |F| ≥ 2. For b ∈ A let w(b) denote the number of sets in F containing b minus the number of sets in F not containing b. Frankl’s conjecture from 1979, also known as the union-closed sets conjecture, states that there exists an element b ∈ A with w(b) ≥ 0. The present paper deals with the average of the w(b), computed over ...

Group valued edge labellings λ of a Bratteli diagram B give rise to a skew-product Bratteli diagram B(λ) on which the group acts. The quotient by the group action of the associated dynamics can be a nontrivial extension of the dynamics of B. We exhibit a Bratteli diagram for this quotient and construct a morphism to B with unique path lifting property. This is shown to be an isomorphism for the...

objectives: herbal medicine is known as a valid alternative treatment. salvia reuterana, which has been used in the iranian traditional medicine, is mostly distributed in the central highlands of iran. salvia reuterana is a medicinal herb with various therapeutic usages. the aim of the present review is to take account of pharmacological properties of salvia reuterana. materials and methods: th...