Although pre-mixed concentrated nutrient solutions are generally purchased from commercial nutrient manufacturers by hydroponic hobbyists and small commercial growers, several tools exists to help anyone prepare their own solutions without extensive knowledge about chemistry.

Although simple programs can be written in a few hours, programs that use complex mathematical formulas whose solutions can only be approximated or that draw data from many existing systems may require more than a year of work.

Although some problems in statistical physics can be solved analytically using approximations and expansions, most current research utilizes the large processing power of modern computers to simulate or approximate solutions.

Although in an open process, anyone may identify and correct such limitations, and the resulting cleaner specification may be used by all vendors, this is more difficult post-facto, as customers already have valuable information and processes encoded in the faulty but dominant product, and other vendors are forced to replicate those faults and quirks even if they could design better solutions, for the sake of preserving interoperability.

Although Germany began to improve economically in the mid-1920s, the Great Depression created more economic hardship and a rise in political forces that advocated radical solutions to Germany's woes.

Although he points out many problems and possible solutions in his paper, he does admit that there is still much to be done to build a strong social capital.

Although the issue of existence and uniqueness of solutions of ordinary differential equations has a very satisfactory answer with the Picard – Lindelöf theorem, that is far from the case for partial differential equations.

Although this result might appear to settle the existence and uniqueness of solutions, there are examples of linear partial differential equations whose coefficients have derivatives of all orders ( which are nevertheless not analytic ) but which have no solutions at all: see Lewy ( 1957 ).

Although the optimal strategy of a game may not ( yet ) be known, a game-playing computer might still benefit from solutions of the game from certain endgame positions ( in the form of endgame tablebases ), which will allow it to play perfectly after some point in the game.

Although it is possible to find some particular solutions of the Navier-Stokes equations governing fluid motion, all such solutions are unstable at large Reynolds numbers.

Although these policies presented high-profile, short-term solutions, the ecological effects of these policies are hotly debated among forestry experts.

( Although HDML is still in use in Japan by KDDI brands such as au, especially for mobile banking solutions.

Although analytical solutions to this problem are scarce, there are upper and lower bounds to these functions including the famous Shannon lower bound ( SLB ), which in the case of squared error and memoryless sources, states that for arbitrary sources with finite differential entropy,

Although hibernating animals have adapted mechanisms to avoid metabolic imbalances associated with hypothermia, hypothermic organs and tissues being maintained for transplantation require special preservation solutions to counter acidosis, depressed sodium pump activity and increased intracellular calcium.

Although originally seeming out of his depth as a Member of Parliament, Ali's bizarre behaviour and solutions seem to actually work.

Although zinc chloride solutions are acidic by the Brønsted definition, the zinc cation also specifically attacks hydroxyl groups as a Lewis acid.

Although wildlife corridors have been proposed as solutions to habitat and wildlife population fragmentation, there is little evidence that they are broadly useful as a conservation strategy for all biodiversity in non-developed or less-developed areas, compared to protecting connectivity as the relevant ecological attribute.

Although it still manufactures computers, it sees the physical goods as a small part of the " business solutions " industry.

Although this leads to great flexibility ( i. e .- any type of desktop can be displayed ), it is often less efficient than solutions that have a better understanding of the underlying graphic layout like X11 or Windows Remote Desktop Protocol.

Although finding solutions to some problems, airline deregulation has created strongly polarizing results.

Although a complete picture cannot be given, we can indicate some aspects of life into which the Christian faith entered as at least one creative factor.

Although the fatty protein molecules, carried in the blood and partly composed of cholesterol, are water soluble, cholesterol itself is insoluble, and cannot be destroyed by the body.

Although BCD is not as widely used as in the past, decimal fixed-point and floating-point formats are still important and continue to be used in financial, commercial, and industrial computing, where subtle conversion and rounding errors that are inherent to floating point binary representations cannot be tolerated.

Although a bee sting can be deadly to those with allergies, virtually all bee species are non-aggressive if undisturbed and many cannot sting at all.

Although water is vital for life, the structure of this water in the cytosol is not well understood, mostly because methods such as nuclear magnetic resonance only give information on the average structure of water, and cannot measure local variations at the microscopic scale.

Although the date of his birth is nowhere recorded, Constantine II cannot have been born any later than the year after his father's death, that is 879.

Although the Ann McKim was the first large clipper ship ever constructed, it cannot be said that she founded the clipper ship era, or even that she directly influenced shipbuilders, since no other ship was built like her ; but she may have suggested the clipper design in vessels of ship rig.

In July 2007, new forensic evidence was presented in the case and a status report jointly issued by the State and the Defense team stated, " Although most of the genetic material recovered from the scene was attributable to the victims of the offenses, some of it cannot be attributed to either the victims or the defendants.

Although the characters ' voices are recorded in a studio, ADR is necessary whenever members of the cast cannot all be present at once.

Although siblinghood is symmetric ( if A is a sibling of B, then B is a sibling of A ) and transitive on any 3 distinct people ( if A is a sibling of B and C is a sibling of B, then A is a sibling of C, provided A is not C ( Note that " is a sibling of " is NOT a transitive relation, since A R B, and B R A implies A R A by transitivity )), it is not reflexive ( A cannot be a sibling of A ).

Although these experiments cannot detect individual gravitons, they might provide information about certain properties of the graviton.

Although the presence of either quicklime or saltpeter in the mixture cannot be entirely excluded, they were consequently not the primary ingredient.

Although identity between the Atlantic and Pacific populations cannot be proven by anatomical data, its skeleton is distinctive and easy to distinguish from that of all other living whales.

Although current pumps can include a glucose sensor, and they cannot automatically respond to meals or to rising or falling glucose levels.

Although they accept that some complex systems and organs can be explained by evolution, they claim that organs and biological features which are irreducibly complex cannot be explained by current models, and that an intelligent designer must have created life or guided its evolution.

Although many have linked one's social origins and educational attainment to life chances and opportunities, education cannot serve as the most influential predictor of economic mobility.

Although there is no obvious restriction that any given regular polygon cannot be a face of a Johnson solid, it turns out that the faces of Johnson solids always have 3, 4, 5, 6, 8, or 10 sides.

Although there is no doubt that most ( but not all ) of the later copies of the Antiquities contained references to Jesus and John the Baptist, it cannot be definitively shown that these were original to Josephus writings, and were not instead added later by Christian interpolators.

Although the kidney cannot directly sense blood, long-term regulation of blood pressure predominantly depends upon the kidney.

Although humans and other mammals use various biosynthetic pathways to both break down and synthesize lipids, some essential lipids cannot be made this way and must be obtained from the diet.

Although the memory manager can recover unreachable memory, it cannot free memory that is still reachable and therefore potentially still useful.

:" Although theoretical calculations can be made today, the eventually attainable range of chemical reaction cycles, error rates, speed of operation, and thermodynamic efficiencies of such bottom-up manufacturing systems cannot be reliably predicted at this time.

Although a DNA molecule cannot exist without physical properties, these properties are constrained by higher level ordering principles.

Although Ueshiba eventually distanced himself from both these teachers, their effect on him and his art cannot be overstated.

Although these postulates cannot be applied in all cases, they do retain historical importance to the development of scientific thought and are still being used today.