We show a matrix A is similar to an orthogonal matrix over a field of characteristic 2 if and only if ( 1 ) the invariant factors of A are symmetic,(2) A has at least an elementary divisor of the form ( x + 1 ) m.

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The invention provides a method for achieving priority level for generating sequence of mapping items which are transformed by network address, the method comprises the following method, first, when an address conversion apparatus needs to converse address after the address conversion apparatus receives a data packet, judging whether the items are generated, upwards sending the data packet to a CPU when a mapping item is not generated, step B, judging whether concurrent mapping number exceeds the preset mapping enqueue threshold with the CPU, if exceeds the preset mapping enqueue threshold, and judging whether a Referer field is contained in HTTP data, and recording the Referer field or a GET field according to judgment result, writing in a REF table, and arraying a priority level for each user according to a write sequence, and step C, leading the CPU to generate map in turn according to the priority level in the REF table, and then sending down to a forwarding layer to transfer a data packet.

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In section one, we introduce some background of the topic, in section two we review some basic and recent results about the structure and hierarchies of the computably enumerable degrees which are closely related to our topic- the algebraic structure of the plus cupping Turing degrees, in section three, we outline the basic principles of the priority tree argument, one of the main frameworks and tools of theorem proving in computability theory, and in section four, we prove a new result concerning the algebraic structure of the plus cupping Turing degrees that there exist two computably enumerable degrees a, b such that a, b ? PC, and the join a V b of a and b is high.

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