About the characterization of a fine line that separates generalizations and boundary-case exceptions for the Second Incompleteness Theorem under semantic tableau deduction

Our previous research showed that the semantic tableau deductive methodology of Fitting and Smullyan permits boundary-case exceptions to the second incompleteness theorem, if multiplication is viewed as a 3-way relation (rather than as a total function). It is known that tableau methodologies prove a schema of theorems verifying all instances of the law of the excluded middle. But if one promotes this schema of theorems into formalized logical axioms, then the meaning of the pronoun of ‘I’, used by our self-referencing engine, changes quite sharply. Our partial evasions of the second incompleteness theorem shall then come to a complete halt.

The Transrational Numbers as an Abstract Data Type

In an arithmetical structure one can make division a total function by defining 1/0 to be an element of the structure, or by adding a new element, such as an error element also denoted with a new constant symbol, an unsigned infinity or one or both signed infinities, one positive and one negative. We define an enlargement of a field to a transfield, in which division is totalised by setting 1/0 equal to the positive infinite value and -1/0 equal to its opposite, and which also contains an error element to help control their effects. We construct the transrational numbers as a transfield of the field of rational numbers and consider it as an abstract data type. We give it an equational specification under initial algebra semantics.

The draughtsman of architecture and engineering in the naval, maritime and fluvial industry of Cartagena

Careers and industry tend to go hand in hand with the references that are formed throughout their history, but there are careers hidden from them, without demeriting their importance in their process and growth. The Architectural and Engineering Draughtsmen are professional technologists who are active in the Naval Industry and little is referred to them as an associated profession. However, for all those who are immersed in this industry, the work they perform and their recognition in supporting the achievement of projects in the different design and construction stages is very clear. What is really worth highlighting in them, is the growth and evolution they have taken in this industry.The times when the draughtsman transcribed ideas into drawings and plans is on the verge of extinction. Today, trained personnel is required and available to develop virtual models giving characteristics associated with the properties of each element and its integration into the total function of the project. These technologists have the experience and specific knowledge in the industry, and become the right hand of designers, engineers and builders, to develop designs from their basic stage to the closure of projects, with the confidence that they can receive alarms and ideas that make possible the completion of each job. For this reason, they take the name of designers or modelers according to the particular case of the company for which they work.

A Modelling Pearl with Sortedness Constraints

Some constraint programming solvers and constraint modelling languages feature the SORT(L,P,S) constraint, which holds if S is a nondecreasing rearrangement of the list L, the permutation being made explicit by the optional list P. However, such sortedness constraints do not seem to be used much in practice. We argue that reasons for this neglect are that it is impossible to require the underlying sort to be stable, so that SORT cannot be guaranteed to be a total-function constraint, and that L cannot contain tuples of variables, some of which form the key for the sort. To overcome these limitations, we introduce the StableKeysort constraint, decompose it using existing constraints, and propose a propagator. This new constraint enables a powerful modelling idiom, which we illustrate by elegant and scalable models of two problems that are otherwise hard to encode as constraint programs.

Groin and hip quandaries

There is little consensus on the diagnosis, pathophysiology, investigation and management of groin injuries. A key factor in making the correct diagnosis is to firstly understand the anatomy and likely generators of pain in the region. This requires an understanding of the two joints in the pelvis – the hip joint and the pubic symphysis ‒ which are at the centre of many movements. There are a multitude of varying studies on this topic. However, most importantly, many of the groin/hip pathologies can be averted by thorough and specific prehabilitation, bearing in mind the entire kinetic chain and addressing total function above and below the pelvis.

Self-Adapting Function Principle and Creative Design of BFT Type

The author summed up the total function of the self-adapting system of slow-footed multiple-flexible driving with overloading by making use of the creative design method of function principle, applied the mechanism of self-adapting to creative design this sort equipment of BFT,funded its false, and proposed way of creative design basing on the total functions.This way has super-performance of self-adapting .It has a good foreground

Groin and hip quandaries

There is little consensus on the diagnosis, pathophysiology, investigation and management of groin injuries. A key factor in making the correct diagnosis is to firstly understand the anatomy and likely generators of pain in the region. This requires an understanding of the two joints in the pelvis – the hip joint and the pubic symphysis ‒ which are at the centre of many movements. There are a multitude of varying studies on this topic. However, most importantly, many of the groin/hip pathologies can be averted by thorough and specific prehabilitation, bearing in mind the entire kinetic chain and addressing total function above and below the pelvis.

Research of the Thought and Method in Function Reserving Design Based on Individuation Degree Evaluation

Thought and method in function reserving design is for realizing the volume-production of individual products, based on the attention of users' individualities. The function tree is built up according to the subdivision of the total function. On this foundation, the method requires all the leaves of the function tree evaluated on their individuation degree by calculating the opening degree, association degree and dependency between the factors and the intimacy and interest degree between function factors and users. According to the result of individual degree evaluation, a rank of individuation degree priority of them is listed to help to decide the proper factors to reserve. By this means, users can participate themselves into the procedure of design, meeting their own individual needs.At last of this paper, the realizability of the thought and method is statemented and a case of lamp design of this method is taken as an example to demonstrate the design procedure.