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LOGARYTMY ZADANIA Z ROZWIZANIAMI PDF

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Existence of solutions for infinite systems of differential equations in spaces of tempered sequences, Electronic Journal of Differential EquationsNo. On moduli of smoothness of Banach spaces zadanix, Notas de Matematicas, Univ. Delta 1, str. On existence and asymptotic stability of solutions of a nonlinear integral equationJ. Existence theorems for some quadratic integral equationsJ. Functions of generalized bounded variationZesz. Zadanie 21 Sinica 13 Solvability of a nonlinear integral equation of Volterra typeJ.

On solutions of some functional-integral equations in Banach algebraMath. On local attractivity and asymptotic stability of solutions of a quadratic Volterra integral equationApplied Mathematics and Computation Nondecreasing solutions of a quadratic singular Volterra integral equation, Mathematical Comput.

Fixed points and solutions of operator equations for the weak topology in Banach algebras, Taiwanese Journal of Mathematics 18 Measures of weak noncompactness and nonlinear integral equations of convolution logzrytmyJ.

Measures of noncompactness related to monotonicityComment. Some properties of moduli of smoothness of sets in the space of continuous functionsBull. Integrable solutions of Hammerstein and Urysohn integral equationsJ. Scandinavica 98 On solutions of infinite systems of integral equations of Hammerstein type, Journal of Nonlinear and Convex Analysis Algunos problemas de la geometria de espacios de BanachUniversidad de La Laguna 3 Carolinae 21 On the solutions of a translation equation on the additive halfgroup of non-negative real numbers, Zeszyty Nauk.

On solutions of a quadratic Hammerstein integral equation on an unbounded domainDynamic Systems and Applications 18 Measures of noncompactness and solvability of an integral equation in the class of functions of locally bounded variationJ. Poland also has one of the lowest water retention rates in Europe, of only ca.

This rate is the ratio of the current, total capacity of the water in retention reservoirs ca. In many European countries this rate exceeds 12 or so percent. A larger capacity of retention reservoirs allows for better water management, and contributes to mitigating the effects of floods and droughts.

A very important indicator of the use of water for various purposes is the amount of water withdrawal. Poland in this respect is very different from the rest of the globe. The main difference relates to agriculture and industry. In Poland the industrial use of water includes cooling turbine condensers in thermal power plants.

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This water after passing through a condenser is returned to a river or reservoir in the same quantity, although with a higher temperature. World-wide agriculture uses irrigation to a large extent, while Polish agriculture is based entirely on rainfall. On a global scale the current water consumption, especially in agriculture, can give rise to serious concern. Hydropower generation Hydropower generation is a very important renewable source of electricity.

On the global scale hydropower plants produce ca. It is worth noting that the electricity generation in hydroelectric power plants, is renewable and does not pollute the environment.

There is no justification for the widespread criticism of hydropower plants by ecologists, because these facilities bring about evident benefits. The same quantity of water which flows into water turbines, flows out downstream. Flowing through the turbine the water is aerated, which is beneficial to the environment. At the turbine inlet racks a lot of garbage flowing in rivers is retained, that must be collected and utilized by hydropower plants.

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Moreover, hydroelectric plants play a very important role in the power system due to their easy turning on and off, as well as the capability to operate below their capacities when flow in the river is lower than the installed one.

One of the most beneficial of Polish complex hydroengineering projects is the Lower Vistula Cascade [3]. Preliminary estimates have shown that the lower Vistula accounts for ca. The first concept of the Lower Vistula Cascade LVC was devised in as a study of the Polish Academy of Sciences and Hydroprojekt summarizing many years of research and design efforts of Polish scientists and hydraulic engineers.

This concept assumed the construction of eight low head barrages with run-of-river reservoirs, large hydropower capacities installed at each barrage, and the total electricity output in an average hydrological year of ca. The total capacity installed at all barrages was 1, MW. KDW LVC was meant to be a compact system of eight barrages with run-of-river reservoirs so situated that head water at the downstream barrage reaches the upstream barrage. In view of limited floodplain areas 7 W.

It was assumed that all power plants would operate as run-of-river facilities. In the s the LVC concept was revisited, but with a slight modification, i. The LVC impact area is inhabited by ca. In addition, there are many important cities in this region, i.

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Economic activity in the region is associated with large plants in the chemical, pulp and paper, and petrochemical industries. There is high unemployment in these areas. The Lower Vistula Cascade is a very complex capital expenditure project relevant to important economic, social and environmental aspects in the area of formerly six, and currently three voivodeships: Mazovian, Kujavian-Pomeranian, and Pomeranian.

The primary LVC function was to be electricity production and inland navigation. The hydropower output is environmentally clean and renewable energy that can fulfil an important intervention and regulation function in the power system. Besides the electricity generation, LVC was meant to fulfil an important navigation function creating an international class navigable waterway across the Lower Vistula River section, i.

Besides the two basic functions of power generation and navigation, it was assumed setting up a stabilized water surface system, which was to serve water intaking for municipal, industrial, and agricultural applications, reducing flood risks, and development of sports, tourism and recreation.

The stable water level in the cascade beneficially impacts the groundwater table throughout the cascade. In , as part of the proposed Lower Vistula Cascade, Wloclawek barrage km was commissioned, with a run-of-river reservoir. The Wloclawek barrage was the first of the proposed power generation and navigation cascade. However, the economic crisis of the s cancelled this project. It is known that inland waterway transport is the most economical, safe and environmentally friendly.

Moreover, the EU now puts great emphasis on the use of this type of transport, even co-financing such investments. Provided, however, that the waterway in question is of an international class, i.

Poland has not signed the convention so far. It is worth noting that this waterway is already operable in Belarus and Ukraine and is of at least the IV class. However, this requires perspective thinking and political will of the government.

The reform of water management assumes an increase in the revenues from hydropower generation. Water management professionals are well aware of the fact that the use of rivers for hydropower generation of navigation entails interference with the aquatic environment. With such an allegation from naturalists and environmentalists we are always confronted when discussing new or even modernized facilities.

The question is: how is it possible that in many EU countries that share the same EU law with Poland new hydroengineering facilities are bulit for water management? The primary water management objective is a comprehensive use of water resources. In this respect we can divide stakeholders into water users and water consumers. Water users include inland navigation, hydropower generation and water recreation that use water, but do not consume it.

Water consumers are municipal and industrial water supply and agriculture. Poland joined the EU in and then uncritically adopted the WFD, while other countries previously belonging to the EU had implemented it for four years already.

LOGARYTMY - Zadania.info

Therefore, WFD does not concern all water management elements, but only some selected sectors. This approach stems from the fact that WFD was drafted in the late twentieth century, when the EU had only 16 Member States, and very rich too. In these countries there was already fully developed hydroengineering infrastructure allowing for extensive use of hydropower generation and inland waterways, and the only problem was the water quality that had to be improved.

In waters in Poland were in a very bad condition, and the hydroengineering infrastructure was insufficient. First, it was necessary to take action to improve water quality by building sewage treatment plants. We had spent lots of money for the construction of sewage treatment plants, but it is only one part of water management. In this situation there were not enough funds for the development or even maintenance and upgrades of existing hydro facilities.

Floods Directive DP came into force in Approach to flooding in the DP is completely different from what it was before.

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It refers to flood risk and its management. Poland is a country with a high risk of flooding, as evidenced by successive floods in , and , which resulted in huge economic, social, and even environmental losses [5]. In this way we know better where the real flood risk is and what should be done. The problem is, however, that regardless of all previous DP implementation efforts, ultimately capital expenditure projects have to be developed in the form of technical solutions and nontechnical activities supporting them.

The future will show how the DP related activities have safeguarded us from floods. It is essential to remember that the construction of new retention reservoirs is an opportunity to build new hydroelectric power plants using new water heads, possible use of inland waterways for shipping by increasing their depths, provision of required water reserves for possible drought, or great opportunities for relaxation, recreation and water sports.

Security, however, is only seemingly unconditional, because the use of symmetric cryptosystems is inherent to the problem of secure key agreement between the parties to secure communication - Alice and Bob. They must somehow directly convey a secret bits, physically meeting together, or using a courier, but in any case due mentioned in the introduction of the fundamental vulnerability of traditional media to eavesdropping , this method does not guarantee absolute security.

The use of an absolutely secure encryption Vernam require to provide the recipient canal classic key with a length equal to the length of the message itself, which in addition can be used only once, and his interception is no more difficult than if the same channel was sent a message in the form of overt - such proceedings seems to so completely does not make sense.

The advantage of this approach is only that can be sent at once a large number of keys using highly secure physical channel which then will be gradually used to encrypt individual messages.

Although the use of the above-described scheme using encryption Vernam is the strongest known now classic scheme secure transfer of information to the impracticality of using the now widely from providing less security codes based on the short key and repeated its use, which, however, fracture, about how many theoretically possible, it is due to the extremely time-consuming technical possibilities.

Symmetric cryptosystem: Common to both participants secret. The identity of the problem of confidentiality of messages with the problem of secrecy of the key the message is secure until the third person does not know the secret key. The problem of key distribution to agree on a key without a third party being away hundreds of kilometers. Scalability for 2 persons is required for key 1 for 3 persons - 3 keys for 4 - 6 keys, Authenticity secrecy of the key does not provide authenticity - can not be formally demonstrate which of the two potential sites is the real sender.

Susceptibility to cryptanalysis techniques, or gradual learning the key. Each symmetric cryptography algorithm may be broken except cipher one-time-pad : Inference often guessing based on the messages contained in the previously captured szyfrogramach.

Inference based on the ciphertext and well-known part of the message explicit. Breaking ciphers with the selected key when the system is followed by frequent changes of key. The algorithm stronger entailing greater computational complexity methods of breaking the greater safety.

Progressing faster exponentially according to Moore's law , the increase in computing power makes cryptanalysis techniques are becoming more efficient. It is not known at which point it turns out that the introduction of increasingly complex symmetric cryptosystems no longer profitable due to the short time of their security, and there are indications that it may become even in a few years' perspective.

They are distinguished symmetric ciphers and block streaming. The encrypted stream ciphers is the entire message once and checked, in block message is divided into blocks typically bit or bit.. In symmetric cipher stream is generated potentially infinite stream encryption, creating a ciphertext c Cipher by performing an XOR operation message m Message and stream encryption s Stream.

Pdf z rozwizaniami logarytmy zadania

Under the influence of work on techniques led by Ralph Merkel, Whitfield Diffie and Martin Hellman presented the key distribution algorithm called the Diffie-Hellman protocol based on a mathematical problem difficult discrete logarithm. A year later, Ron Rivest, Adi Shamir and Len Adelman based on the ideas developed asymmetric cryptosystem which their initials was named RSA based on the problem of factorization into prime factors of numbers.

With the decryption key, which in the case of applications to ensure the secrecy of communication is the secret ie. The private key , you can easily in terms of computational complexity to obtain the encryption key that being completely open, is called. Public key. However, to obtain the decryption key private with the encryption key the public is no longer a problem mathematically difficult.

Public key encryption can be passed explicitly side that wanted to send a secret message. Security scheme is based on the computational complexity issues factorization of numbers, which is crucial in solving the problem of discrete logarithm.

There is no evidence, however, to the present, whether known modern factorization algorithms provide the smallest possible complexity, and if there are simpler ways of solving this issue.

Pdf z logarytmy zadania rozwizaniami

Furthermore, the known algorithms are now quantum Shor'a quantum factoring algorithm , which provides exponential acceleration, making the problem of factorization computationally easy; However, their practical use goes far beyond current technological capabilities.

In this scheme, Alice generates a pair of keys - public and private, then 13, making public key mainstream. Bob wanting to send a message to Alice, encrypts it using the public key, so that it can be decrypted only by Alice, which was the only one who knows your private key.