2. Material and methods

2.2. Assumptions and notions

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2.2.1. Assumptions
In this paper, the mathematical model is developed with the following assumptions
The planning horizon is finite.
Replenishment rate is infinite.
Single item inventory control.
Demand and deterioration rate are constant.
Deteriorating occurs as soon as the items are received into inventory within 0,t_n.
The shortage is not allowed.
The leading time is nonzero.
The purchasing cost is more than the holding cost.
The inventory level is constant within the second component of first run time, non zero within the planning horizon.
The total relevant cost consists of fixed ordering, purchasing and holding cost.

2.3. Notation

D= The demand rate quantity in period 0,t_n.
Q_1= The quantity within A, B.
Q_M= The quantity within 0, A
t_1= The first component of the first runtime.
t_w1= The first leading time.
t_m1= The second component of the first runtime.
Q = The total quantity within 0, B.
TC_A = The total fixed ordering cost during 0, t_n.
I_h=The holding cost.
TC_h = The total holding cost during 0, t_1 .
TC_P = The total purchasing cost during 0,t_1.
TC= The total relevant cost during 0,t_1.

2.4. Parameters

T = The length of the finite planning horizon.
I_1 (t) = The inventory level at time 0,t_m.
I_2 (t) = The inventory level at time t_m ,t_1 .
? t?_1 = The first run time of replenishment.
? = The constant deteriorating rate units/unit time during 0,t_1 .

3. Mathematical model

2.6 GENOME PLASTICITY AND EVOLUTION OF ESCHERICHIA COLI
Like all life forms, new strains of E. coli evolve through the natural biological processes of mutation, gene duplication, and horizontal gene transfer; in particular, 18% of the genome of the laboratory strain MG1655 was horizontally acquired since the divergence from Salmonella. E. coli K-12 and E. coli B strains are the most frequently used varieties for laboratory purposes. Some strains develop traits that can be harmful to a host animal. These virulent strains typically cause a bout of diarrhea that is often self-limiting in healthy adults but is frequently lethal to children in the developing world. (Futadar et al., 2005). More virulent strains, such as O157:H7, cause serious illness or death in the elderly, the very young, or the immunocompromised.
The genera Escherichia and Salmonella diverged around 102 million years ago (credibility interval: 57–176 mya), which coincides with the divergence of their hosts: the former being found in mammals and the latter in birds and reptiles. (Wang et al., 2009). This was followed by a split of an Escherichia ancestor into five species (E. albertii, E. coli, E. fergusonii, E. hermannii, and E. vulneris). The last E. coli ancestor split between 20 and 30 million years ago.
The long-term evolution experiments using E. coli, begun by Richard Lenski in 1988, have allowed direct observation of genome evolution over more than 65,000 generations in the laboratory. For instance, E. coli typically do not have the ability to grow aerobically with citrate as a carbon source, which is used as a diagnostic criterion with which to differentiate E. coli from other, closely, related bacteria such as Salmonella. In this experiment, one population of E. coli unexpectedly evolved the ability to aerobically metabolize citrate, a major evolutionary shift with some hallmarks of microbial speciation.
2.7 INCUBATION PERIOD
The time between ingesting the STEC bacteria and feeling sick is called the “incubation period”. The incubation period is usually 3–4 days after the exposure, but may be as short as 1 day or as long as 10 days. The symptoms often begin slowly with mild belly pain or non-bloody diarrhea that worsens over several days. HUS, if it occurs, develops an average of 7 days after the first symptoms, when the diarrhea is improving.

2.7.1 DISCOVERY OF ANTIBIOTICS
• History of antibiotics – 1
19th century:Louis Pasteur & Robert Koch
• History of antibiotics – 2
Plant extracts
– Quinine (against malaria)
– Ipecacuanha root (emetic, e.g. in dysentery)
Toxic metals
– Mercury (against syphilis)
– Arsenic (Atoxyl, against Trypanosoma)
• Dyes
– Trypan Blue (Ehrlich)
– Prontosil (azo-dye, Domagk, 1936)
• History of antibiotics – 3
Paul Ehrlich
• started science of chemotherapy
• Systematic chemical modifications
(“Magic Bullet”) no. 606 compound = Salvarsan (1910)
• Selective toxicity.
• Developed the Chemotherapeutic Index
• History of antibiotics – 4
Penicillin- the first antibiotic – 1928• Alexander Fleming observed the
killing of staphylococci by a fungus (Penicillium notatum)
• observed by others – never exploited
• Florey & Chain purified it by freeze-drying (1940) – Nobel prize 1945
• First used in a patient: 1942
• World War II: penicillin saved 12-15% of lives
• History of antibiotics – 5
Selman Waksman – Streptomycin (1943), was the first scientist who discovered antibiotic active against all Gram-negatives for examples; Mycobacterium tuberculosis
– Most severe infections were caused by Gram-negatives and Mycobacterium
tuberculosis, extracted from Streptomyces – extracted from Streptomyces
– 20 other antibiotics include. neomycin, actinomycin
2.8 CHARACTERISTICS OF ANTIBIOTICS
According to the Oxford Dictionary, the term Antibiotics encompasses medicines (such as penicillin or its derivatives) that inhibit the growth of or destroys microorganisms. Antibiotics are naturally occurring substances that exhibit inhibitory properties towards microbial growth at high concentrations. (Zaffiri, et al., 2012).
-Antibiotics are selective in their effect on different microorganisms, being specific in their action not only against genera and species but even against strains and individual cells. Some of these agents act mainly on gram-positive bacteria, while others inhibit only gram-negative ones.
-Some antibiotics are produced by some organism, from different strains of penicillin.
-Bacteria are sensitive to the antibiotic which enable them to developed resistance after contact, for several periods.

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2.9 ROLE OF ANTIBIOTICS
Based on the clinical use of antibiotics, it may appear that these compounds play a similar role as microbial weapons in nature, yet this seems unlikely due to the fact that the concentrations used in the clinical setting are significantly higher than that produced in nature (Fajardo et al., 2008). Due to experimental evidence, it makes more sense to see antibiotics as small, secreted molecules involved in cell-to-cell communication within microbial communities.
(Martinez, 2008). Diverse Studies have been conducted in which different antibiotics and antibiotic-like structures were administered to different bacterial species at levels below the compounds minimum inhibitory concentrations (MIC). (Fajardo et al., 2008). that was

2.1 Introduction
The study of Geotechnical Earthquake Engineering requires an understanding of the various processes by which earthquakes occur and their effects on ground motion. The field of seismology developed from a need to understand the internal structure and behavior of the earth, particularly as they relate to earthquake phenomena. Although earthquakes are complex phenomena, advances in seismology have produced, a good understanding of the mechanisms and rates of occurrence of earthquakes in most seismically active areas of the world.
What is an Earthquake?
Earthquake: an event of ground shaking usually caused by the rupturing of a fault within the Earth. In other way the earthquake is defined as Unpredictable natural phenomenon of vibration of the ground. It becomes one of the most devastating natural hazard only if it’s considered in relation with structures.
What is Earthquake Engineering?
The earthquake has begun to become a problem for humans since they started to build structures. The deaths and the damage to buildings that they cause have several economic, social, psychological and even political effects. A general study of earthquakes involves many scienti?c disciplines that deal with the problem: Seismology ?? Engineering ?? Economy ?? Psychology
Earthquake Engineering : Branch of engineering devoted to mitigating earthquake hazards. It covers the investigation and solutions of the problems created by damaging structures.
Why Do Earthquakes Occur?
Earthquakes occur due to:
• Sudden formation of a new fault (fracture on which sliding occurs)
• Sudden slip on an existing fault
• Sudden change in the arrangement of atoms in the minerals of a rock
• Movement of magma in a volcano
• Explosion of a volcano
• Giant landslides
• Meteorite impact
• Underground nuclear bomb tests
2.1.1 Earthquake Terminology:
• Hypocenter (Focus): actual location of the earthquake at depth.
• Epicenter: location on the surface of the Earth above the hypocenter.

Figure 2.1 Origin of Earthquake
• Fault Plane – the plane along which the rock or crustal material has fractured
• Hanging Wall Block – the rock material which lies above the fault plane
• Footwall Block – the rock material which lies below the fault plane.
2.1.2 Causes of Earthquakes
There are basically three types:
• Volcanic
• Tectonic
• Collapse
Tectonic Earthquakes: Most earthquakes occur at plate margins due to tension, compression or shearing forces. Rocks at plate margins are in constant motion and are being pushed, pulled, bent, twisted and folded. Inevitably at some point they must break or crack to produce FAULTS!!
What is a Fault?
A fault is a break or fracture between two blocks of rocks in response to stress. There are three types of stresses produce in faults (1) Tension (2) Compression (3) Shear
2.2 Faults
Theory of plate tectonics generally assigns the relative movement of plates to one of the three preceding types of plate boundaries; examination on a smaller scale reveals that the movement at a particular location can be quite complicated. In some regions, plate boundaries are distinct and easy to identify, while in others they may be spread out with the edges of the plates broken to form smaller platelets or microplates trapped between the larger plates. Locally, the movement between two portions of the crust will occur on new or preexisting offsets in the geologic structure of the crust known as faults.
Faults may range in length from several meters to hundreds of kilometers and extend from the ground surface to depths of several tens of kilometers. Their presence may be obvious, as reflected in surficial topography, or they may be very difficult to detect. The presence of a fault does not necessarily mean that earthquakes can be expected; movement can occur a seismically, or the fault may be inactive.

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2. The Working Definitions of Inculturation ( Inculturation in Actions)
The first assembly of the Federation of Asian Bishop Conferences in April, 1974 spoke of an indigenous and inculturated Church. But the 32nd Congregation of the Society of Jesus in 1975 used the actual word “inculturation” in its texts and included a decree on inculturation. In response to this decree, the Jesuit Superior General, Fr. Pedro Arrupe issued a letter to the whole Society on the subject of incultuation on 15 April, 1978. The word “incultuaration” first appeared a papal document of Pope John Paul II, Catechesi Tradendae in 1979. The concept — a neologism — designates the process of incarnating the Christian message and faith into a particular culture. Attempts to offer a befitting definition of inculturation must take into account the following: first, the historical background and development of the concept in ecclesiastical circles; second, the concept’s analogical application as compared to similar concepts in the social sciences whence it was coined.
With its history akin to the call for “aggiornamento,” inculturation has been linked to popular terms like cultural adaptation, localization and indigenization, contextualization, enculturation, acculturation, and to some extent also transculturation and deculturation. Each of these terms refers to a particular relationship between liturgy and culture and idea of interaction between and among two or more cultures. According to Edward Burnette Tylor, culture is defined as “complex whole which includes knowledge, belief, art, morals, law, customs, and many other capabilities and habits acquired by man as a member of society.”
Marcello de Carvalho Azevedo’s definition of culture underscores the general understanding of culture as follows: 1) culture is a creation of a community of people; 2) culture is historically constituted, and transcends a community of people; 3) though imbued with stability, culture precipitates change in society; 4) Culture thrives and improves itself through contact with other cultures and the ensuing cultural osmosis.” Rooted in these general understanding are the following metaphors – “indigenization,” “incarnation,” “adaptation, “accommodation” and “acculturation,” all of which foreground “inculturation.”
Indigenization, derived from the word “indigenous,” refers to the process of conferring on Christian liturgy a cultural form that is native to a local community. Duraiswami Simon Amalorpavadass advanced the use of this term in the liturgy in the 1970’s. According to Anscar Chupungco, what Amalorpavadass really meant was “adaptation” of the Christian liturgy in the framework of the culture of India. In this regard, Chupungco explained that indigenization aims “to give to our liturgy a more Indian setting and complexion and for Chupungo “indigenization” is another word for “Indianization.”
Incarnation is Vatican II’s variation of adaptation. Article 10 of Ad Gentes states that: “As Christ became a Jew in all things save sin, so the Church should become not merely a Church but the Church of a particular locality by virtue of Christ’s incarnation” Incarnation, both as a Christian mystery and a technical term, enriches our understanding of the concept of adaptation. Incarnation takes place when the church and its liturgy embody a community’s culture. As a technical term, incarnation gives depth to adaptation, which is often understood as a work of external adjustment to conformity with a situation. For Ruy Costa, incarnation implies that liturgical forms develop from within the experience of the local church.
The term ‘adaptation’ is the process of integration of the Gospel values into a particular culture. According to Schineller, Pope John Paul II supported the Church’s position on its use when he states: “An adaptation of the Christian life in the fields of pastoral, ritual, didactic and spiritual activities is not only possible, it is even favored by the Church” Adaptation and accommodation are more often applied to the liturgical renewal and reform initiated in the Sacrosanctum Concilium. Adaptations “impart an even increasing vigor to the Christian life of the faith” and “strengthen whatever can help to call” God’s people “into the Church’s fold.” Accommodation is more radical, and concerns elements from the traditions and genius of individual people which could be appropriately admitted into divine worship. Accommodation requires a lot more maturity, time and effort by ecclesiastical authorities.
Acculturation, according to Aylward Shorter is, “the encounter between one culture and another, or the encounter between cultures in mutual respect and tolerance.” But he strongly states that the encounter happens on an external basis which may lead to juxtaposition of unassimilated cultural expression coming from various directions or origins.” Nevertheless, an encounter between cultures is a process that starts with external contact. Shorter gives clear utterance to one of the basic principles of cultural anthropology, when he affirms that “acculturation is a necessary for inculturation.” This process implies the presence of multiple cultures or cultural realities. This, therefore, may be used in analogy for the process whereby the church, introducing the gospel and faith into a culture, assumes traits and values from the culture, both as communicative vehicles and wealth for itself, thus unfolding more and more its universal character.
Azevedo defines inculturation as “the dynamic relation between the Christian message and culture or cultures; an insertion of the Christian life into a culture, an on-going process of reciprocal and critical interaction and assimilation between them.” Crollius also defines inculturation as “the integration of the Christian experience of a local Church into the culture of its people and becoming a force to animate, orient and innovate the same culture into a new unity and communion.”
According to Shorter, inculturation is “the creative and dynamic relationship between the Christian message and a culture or cultures.” Chupungco defines liturgical inculturation as “the process of inserting the texts and rites of the liturgy into the frame work of the local culture.” Shorter and Chupungco’s definitions emphasize inculturation as a process, privileging the concept’s pastoral nature.

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