Abstract: The widespread problem of **infant** malnutrition in developing countries has stirred efforts in research, development and extension by both local and international organizations. As a result, the formulation and development of nutritious weaning foods from local and readily available raw materials, which are cost effective has become imperative in many developing countries. Thus, the local and readily available raw materials were used to compound and develop nutritious new **infant** **formulae**. The materials used for this study include maize, millet, cowpea, pumpkin, fingerlings and fish bone. The materials were dried and blended to powder. The powders were weighed in the ratio of 4:4:4:3:1:1 respectively and were then mixed properly. Analysis of nutritive value was performed on the **formulae** and compared with NAN-2 (control) and results revealed that the **formulae** had reasonable amount of moisture, lipids, carbohydrate, protein and fibre. Although NAN-2 was superior in carbohydrate and protein, our **infant** formula was higher in mineral elements, vitamins, fibre and lipids. All the essentials vitamins and both macro and micro minerals were found in appreciable quantity capable of meeting the biochemical and physiological demand of the body while the anti-nutrients composition were significantly (p<0.05) below FAO and WHO safe limits. Finally, the compounded **infant** **formulae** was feed to a set of albino wistar rats, while some other set of rats was feed with NAN-2 for the period of twenty seven (27) days and body weight gains were measure at three days intervals. The results of body weight changes was spectacular as their body weight over shot or almost double that of those animals that were feed with NAN-2 at each point of measurement. The results suggest that the widespread problem of **infant** malnutrition in the developing world especially among the low income segment of the society can now be reduced, if not totally eradicated since nutritive and cost effective weaning **formulae** can be prepared locally from common readily available materials.

Human milk is widely recognized as the optimal source of nutrition for infants. Greater scientific understanding of the beneficial components and properties of human milk has contributed to improvements in **infant** formula for in- fants who are either partially or exclusively formula-fed. The bifidogenic properties of human milk are of par- ticular interest, based on evidence that a bifidobacteria- predominant gut microbiota may reduce the risk of infections and allergies in infants [1-4]. Efforts to achieve similar benefits in infants who receive formula have largely focused on the addition of either probiotics or prebiotics, or both, to **infant** formula. Probiotics are live bacteria (often bifidobacteria and lactobacilli species) considered to have beneficial health effects [1,2]. Prebiotics are oligosac- charides that pass undigested through the small intestine in humans and are then selectively digested by potentially beneficial bacteria in the colon, such as bifidobacteria [5].

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To evaluate the extent of this overestimation and the limit of its applicability, in the present work a comparative evaluation was made between the third derivative spectrophotometric procedure (thiobarbituric acid method, TBA- test) and the derivatization with 2,4-dinitrophenylhydrazine followed by HPLC-DAD analysis [23-26]. Different commercial types of **infant** milk **formulae** were analysed together with bovine and human milks. Different clean-up steps, extraction procedures and analytical methods were applied. This investigation allowed verifying the reproducibility and accuracy of the procedures. Furthermore the contents of malondialdehyde in cow milk, characterised by a very low unsaturated lipid fraction, and in human milk, the golden standard for feeding of newborns, were compared with the levels found in **infant** **formulae**.

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There was a variation in the absorbance value with respect to the concentration of the heavy metal element and therefore, a strong positive linear relationship is present between the two parameters (r=0.9986). The low LOD and LOQ values demonstrate that the MP-AES method for the analysis of heavy metal elements is highly sensitive (Table 1). The heavy metal content varies widely due to many factors such as differences between food type, characteristics of the manufacturing practices and processes and possible contamination during processing. The present study demonstrated wide variations in the concentrations of most essential and toxic elements in **infant** **formulae** and foods (Table 3). In **infant** **formulae**, the manufacturer’s fortification of essential elements resulted in concentrations many times higher than those found in foods especially Fe, Zn and Cu. The concentration of nickel in the samples, ranging from 0.63 mg/kg to 1.07 mg/kg exceeded the reference value of 5 µg/kg bw/day set by the Food and Agriculture Organization/World Health Organization (FAO/WHO) Joint Expert Committee on Food Additives (JECFA) [24] as the daily intake of Ni through **infant** **formulae** ranged from 7 µg/kg bw day to 19 µg/kg bw day. Mehrnia and Bashti [25] reported daily intake values of nickel through **infant** formula more than tenfold the reference value set by JECFA. Nickel toxicity is associated with immediate and delayed hypersensitivity reactions and has the potential to cause immunological distrubances and act as an immunotoxic agent in humans [26] (Aguzue, Kakulu & Thomas, 2014). Only one sample was contaminated with Hg at a concentration of 0.7 mg/kg. Since Hg was detected in a pear-based food, the presence of methylmercury is excluded as this bioaccumulates in fish. Therefore this value cannot be compared to the EFSA [27] establishing TWI reference value of 1.3 µg/kg b.w. for methylmercury. Cruz and coworkers [28] reported **infant** **formulae** testing positive for Mercury with levels of 0.63 mg/kg and 0.83 mg/kg.

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In powder **infant** **formulae**, the observed bimodal peak maybe the result of the spray- drying process. Thus, the fat globules are disrupted during spray drying and then (i) caseins/heat denatured whey proteins complexes adsorb onto the new expanded lipid droplet interface (Michalski and Januel, 2006) or (ii) the fat globules are attached to each other by casein micelledenatured whey aggregates and a short-chain-like structure is formed (Guo et al., 1998). All this results in the formation of larger particles affecting the surface protein coverage, given the incidence of coalescence of “uncovered fat” occurring at the surface of powder particles (Ye et al., 2007). Moreover, newly uncovered surface on the fat globules may come into contact at the air-water surface of the drying droplet, with the result of some fat spreading easily on the powder particles surface (Ye et al., 2007, Walstra, 1995). The amount of damage fat in the powder samples may have an impact on the digestion in the **infant**.

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The objective of this review was to update evidence on the effects of supplementation compared with non-supplementation of **infant** **formulae** with B lactis and/or LGG on the growth of healthy infants. It was not designed to evaluate the effects of supplementation compared to breast milk. As it is desirable that growth measurements should be taken during the period when **infant** formula remains an exclusive source of nutrition for an **infant**, we focused on supplementation during early infancy. In general, B lactis supplementation results in growth similar to what is found in unsupplemented infants. Caution is needed not to over-interpret these results as in some of the studies only a subset of infants was available for analysis. With regard to LGG supplementation, data limited to only one trial suggest that infants who received **infant** formula supplemented with LGG grew better. The interpretation of these findings is difficult. First, the groups were not equivalent at entry into the study. Second, the mechanisms as to how LGG supplementation might influence weight and length gain are not clear. Finally, no such effect was

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In the previous section, we reduced our problem of finding all **formulae** with k full multiplications for evaluating a given bilinear map to a linear algebra problem: given a finite subset G of a K-vector space V and a target subspace T = Span(T ) of Span(G), we want to find all the rank-k subspaces W of V containing T and which can be generated by elements of G only (i.e., Span(W ∩ G) = W ). One should note that this linear algebra problem is more general than the original problem of optimizing the computation of bilinear maps.

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The considerations and **formulae** of the article can be used in various fields of human activity, including pure and applied science, economics and business, risk management, measuring the implicit risks, hedging financial risks, computing "capital charges that are required to cover unforeseen and extreme financial market fluctuations" (see Caporin and McAleer, 2010).

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Utilizing a method brieﬂy hinted in the author’s paper written in 1991 jointly with V. C. Harris, we derive here a number of unpublished recursion **formulae** for a variety of product partition functions which we believe have not been considered before in the literature. These include the functions p ∗ (n; k, h) (which stands for the number of product partitions of n > 1 into k parts of which h are distinct), and p ∗ (d) (n;m) (which stands for the number of product partitions of n into exactly m parts with at most d repetitions of any part). We also derive recursion **formulae** for certain product partition functions without the use of generating functions.

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The subject of expansion **formulae** of generalized hypergeometric functions occupies a vital position in the literature of special functions. Certain two-dimensional expansion **formulae** of generalized hypergeometric functions participate major role in the growth of the theories of special functions and two-dimensional boundary value problems.

Hart-Smith [1] developed a set of closed form strength **formulae** for a semi-empirical approach to determine the net tension strength of multi-row bolted connections with composite materials. Mottram [2] showed that, for a pultruded fibre reinforced polymer material, the approach to be reliable (and conservative) for the configuration comprising two rows with a single bolt per row. This led to the **formulae** being developed into clauses in an American pre-standard for Load and Resistance Factor Design (LRFD) of Pultruded Fiber-Reinforced Polymer (FRP) Structures [3]. Because the expressions in the Hart-Smith **formulae** are not simple, the message coming from the practitioners, on the ASCE/SEI Fiber Composites And Polymers Standards committee (FCAPS) tasked with developing the pre-standard [3] into a standard, is that they would not use them when designing bolted connections. Taking stock of the specified geometries, bolt details and design parameters permitted by the pre-standard [3] the author conducted an analytical parametric study using the Hart-Smith **formulae** with the aim of establishing simplified forms that could be routinely used in the design office. Presented in this paper is the provenance to this code-specific work when the connection has more than a single row of bolts. A presentation is given to what has been lost, in terms of calculated net tension strength, by providing the simplified strength formula in the mandatory part to the standard. To enable the designer to be able to take full advantage of the Hart-Smith design approach [1, 2], the ‘complicated’ **formulae** and their accompanying mandatory-style text are to be found in an appendix with the standard’s commentary [3].

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Abstract—Existing Block Backward Differentiation **Formulae** (BBDF) of different orders are collected based on their competency and accuracy in solving stiff ordinary differential equations (ODEs). The strategy to fully utilize the **formulae** is optimized using variable step variable order approach. The improved performances in terms of accuracy and computation time are presented in the numerical results with different sets of test problems. The comparison is made between the proposed method and MATLAB’s suite of ordinary differential equations (ODEs) solvers namely ode15s and ode23s.

They can operate this trainer device in two modes. In first mode, each push button is allotted to a specific category of mathematics viz., Algebra, 2D and 3D Geometry, Trigonometry etc. A Braille script is given as a label just beside each pushbutton as in Fig. 5. The user will select the category recognizing Braille script given on the keys and pushes the button to listen to the **formulae**.

Many more congruence is solved by a number of mathematicians establishing **formulae** or algorithmic methods. Even then many more congruence is yet remains to formulate. The author has successfully formulated many such congruence. Here, three congruence are considered for formulation. No method or formula is found in the literature of mathematics. Without using any formula, such congruence becomes more complicated to find solutions. In [1], Problem-7, page-115, a problem is found: If , = 1 , and p is prime such that ≡ 2 3 , then the congruence ≡ , has the unique solution ≡

The four components outlined above, BAC, PV, EV and AC, allow current and future performance to be assessed. The **formulae** below are the core elements of EV, most standards include more sophisticated measures in addition to these. The formula can be used for the whole of the work to date (cumulative), for a set time period or for a defined element of the work (eg, a work package).

Probabilistic sensitivity analyses were performed to esti- mate the distribution of expected INHS costs (Figure 2) and parents’ costs (Figure 3) over 18 months from starting a formula and probability of developing tolerance to cow’s milk by 18 months. Using these distributions, the probabil- ity of each formula being cost-effective at different cost- effectiveness thresholds was estimated (Figures 4 and 5). These graphs showed that the probability of eHCF + LGG being cost-effective was greater than with the other **formulae** for both IgE-mediated and non-IgE-mediated allergic infants, from the perspective of both the health service and parents. Moreover, these graphs suggest that neither eHCF, SBF, HRF, nor AAF would afford a cost-effective use of resources when compared with eHCF + LGG.

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creation, activation or retrieval of movement **formulae**. These **formulae** represent the idea of a movement as a visual or acoustic image and are stored in the left parietal lobe. The left prefrontal area subsequently associates these **formulae** with an inherently stored innervatory pattern to transfer the information to the left primary motor areas. The corpus callosum transfers this information to the right motor cortex if the movement is to be executed by the left limb [3]. Based on some recent clinical evidence we hypothesize that the cerebellum forms an intrinsic part of this connectionist model of Liepmann.