Equivalent conditions of a Hardy-type integral inequality related to the extended Riemann zeta function
Abstract. By the use of techniques of real analysis and weight functions, we obtain two lemmas and build a few equivalent conditions of a Hardy-type integral inequality with a non-homogeneous kernel, related to a parameter where the constant factor is expressed in terms of the extended Riemann zeta function. Meanwhile, a few equivalent conditions for two kinds of Hardytype integral inequalities with the homogeneous kernel are deduced. We also consider the operator expressions.
On inequalities of Hilbert's type
By introducing the function 1/(min{x, y}), we establish several new inequalities similar to Hilbert's type inequality. Moreover, some further unification of Hardy-Hilbert's and Hardy-Hilbert's type integral inequality and its equivalent form with the best constant factor are proved, which contain the classic Hilbert's inequality as special case.
Unity Identity Text Self
Abstract Understanding the receptivity of literature, how one work admits many readers, begins with an analogy: unity is to text as identity is to self. Unity here means the way all a text’s features can be related through one central theme. Identity describes a person’s sameness within different behaviors as variations on one identity theme (Lichtenstein). To find unity or identity, however, the interpreter himself plays a behavioral variation on his identity theme. In interpreting, his identity re-creates itself as he shapes the text to match his characteristic defenses, fantasies, and coherences. Thus, what a poet says about fictional, political, or scientific texts expresses the same identity theme as the poems he writes. To understand reading, criticism, and any knowing or making in symbols, then, we need to let go the Cartesian craving for objectivity and accept the themes in ourselves with which we construe the world—including literary works.